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CIHM/ICMH 

Microfiche 

Series. 


CIHM/ICMH 
Collection  de 
microfiches. 


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10X 

14X 

ISX 

22X 

26X 

30X 

K 

12X 

16X 

20X 

24X 

28X 

32X 

ails 

du 

tdifier 

une 

nage 


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or  illustrated  impression. 


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empreinte. 


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shall  contain  the  symbol  — ^>  (meaning  "CON- 
TINUED"), or  the  symbol  V  (meaning  "END"), 
whichever  applies. 


Un  des  symboles  suivants  apparaitra  sur  la 
dernidre  image  de  cheque  microfiche,  selon  le 
cas:  le  symbole  —^  signifie  "A  SUIVRE  ".  le 
symbole  V  signifie  "FIN". 


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different  reduction  ratios.  Those  too  large  to  be 
entirely  included  in  one  exposure  are  filmed 
beginning  in  the  upper  left  hand  corner,  (eft  to 
right  and  top  to  bottom,  as  many  frames  as 
required.  The  following  diagrams  illustrate  the 
method: 


Les  cartes,  planches,  tableaux,  etc.,  peuvent  dtre 
film^s  d  des  taux  de  reduction  diffdrents. 
Lorsque  le  document  est  trop  grand  pour  dtre 
reproduit  en  un  seul  clichd,  il  est  filmd  A  partir 
de  i'angle  sup^rieur  gauche,  de  gauche  d  droite. 
et  de  haut  en  bas,  en  prenant  le  nombre 
d'images  ndcessaire.  Les  diagrammes  suivarits 
illustrent  la  m6thode. 


rrata 
o 


selure, 
1  d 


a 


32X 


1 

2 

3 

1 

2 

3 

4 

5 

6 

1 


¥*»iwfwpsw^'-  mm^: 


w^^ 


'!!'  i:i.^;iii|ii'f|.i,i;  ,.;i 


INVtISTlGATION 


o» 


ANCE  OF  THE  SUN 


/!« 


AMD  or  TUB 


II tS  WHICH  DEPENB  UPON  IT, 


numtsot 


Oai«llVATIO»S  OF  MARS, 


MAOC  DCniM  THK 


)f ?#If ION  (JF  18e«,  ANR^FROM  Of 8]gR  SOtJRCIf 


i'-M'J 


js:^-' 


1X^1 


f^ 


■\w,-f-»^ 


APPENDIX   11. 


INVESTIGATION 


KK  rill 


DISTANCE  OF  THE  SUN, 


\N1»   l>K  TIIK 


ELEMENTS  WHICH  DEPEND  UPON  11. 


lUO.M    IMI, 


OBSERVATIONS  OF  MARS, 


MADK.    l)IRIN<i     I'lIK 


OPPOSITION  OF  mt  AND  FROM  OTHER  SOURCES. 


BY   SIMON    NEWCOATJi, 

Professor  of  Mathematics,  V.  S,  Navy. 


WASH  IN(}T()N: 

GOVERNMENT     PRINTING     0  F  F  f  C  E. 
18  0  7 


/ 


<'J 


'^J 


"x 


'>.f 


x  ^H 


AI'PKNDIX   II 


1 N V  EST  Id  AT  I  ON 


or  Til 


DISTANCE    OF    THE    SI   N 


AM>  or 


THE  ELEMENTS  WHICH  DEPEND  UPON  IT. 


About  ten  voars  since,  iistroiiDiiKirs  lu',i!;iui  to  susiu-rt  tlmt  Knekc's  viiliic  of  the  Sim's  ilis- 
tiiiK'O,  deduced  tVoia  t!io  Irinisits  of  Veimsiiillic  years  ITCl  and  ITCi),  was  lar-;ely  in  error. 
Tlie  different  nn'tiioils  available  for  its  correction  all  agreed  in  indicating'  a  diininntion  of 
between  one  twenty-fifth  and  oiie-tidrtietli  ol'  the  whole  distance.  Tiie  last  doubt  of  liu!  cor- 
rectness of  the  suspicion  was  removed  by  the  jjublication  of  I'owalky's  paper  on  the  Transit  of 
1769.  In  this  paper  it  was  shown  that,  with  our  more  accurate  kiiowIed-;e  of  the  positions  of 
the  observing  stations,  the  results  of  this  Transit  agreed  with  those  of  the  modern  measures. 

The  magnitude  of  the  correction  being  such  as  seriously  to  alTcct  rhe  reduction  of  meridian 
observations  of  Mercury,  Venus,  and  Mars,  as  well  as  our  coniput  itions  of  the  mass  of  the 
Eartli  and  the  parallactic  equation  of  the  Moon,  it  becomes  important  to  (h^terinine  it  with  pre- 
cision, even  in  advance  of  the  coming  transits  of  Venus.  In  siudi  a  determination  the  results  of 
all  methods  which  can  be  relied  on,  or  the  precision  of  which  can  be  estimated,  ought,  I  con- 
ceive, to  be  combined  in  the  final  result.  Let  us,  then,  glance  at  tiie  various  methods  now 
available. 

1.  By  Observations  of  TromUsof  Fc«(/.s".— This  method  has  gone  into  our  school-books  as  the 
one  superior  to  all  others  in  the  precision  of  its  results.  It  is  true  that  transits  which  occurred 
a  centurv  ago,  when  the  art  of  observation  was  in  its  infancy,  have  furnished  the  solar  parallax 
which  iuis  hitherto  been  adopted  as  the  standard.  It  is  also  possible  that,  should  the  civilized 
world  take  due  interest  in  the  observation  of  the  next  two  transits,  and  sliould  circumstances 
prove  favorable,  the  precision  of  either  result  may  exceed  that  of  any  other  one  determination. 
But  it  is  certain  that  our  modern  determinations  by  other  methods  are  more  [)recise  than  any 
that  can  be  derived  from  the  pas'  transits  of  Venus,  and  opportunities  which  occur  in  but  one 
generation  of  men  out  of  four  are  too  rare  to  bo  implicitly  relicMl  on  in  future. 

2.  From  Observations  of  3Jars  ivhen  near  the  Earth.— Thvce  methods  of  making  these  obser- 
vations have  been  employed. 

«.  By  nearly  simultaneous  observations  of  difference  of  declination  between  Mars  and  a 
neighboring  star,  at  Observatories  situated  in  different  hemispheres  of  the  earth,  and  by  means 
of  Equatorial  Telescopes.      For  the  employment  of  this  method  the  United  States  Astronomical 


'^\. 


INVKSTKiATloN    OF    THK    DIS  !A\('K    Ol"    TirK    SUN 


Kxpcditidii  to  Chili  \v;is  (H^niii/.i'il,  It  was  a^uiii  |ii(i|ii)S((l  hy  Captain  (lilliss.  in  1  Sll-J,  ami 
til>scrvatiniiM  in  this  way  ucic  niailc  at  l'|isala,  liL'idrn,  ami  Wiisliiiigtoii,  in  tlio  N'nitlicrii  Iloin- 
is|ili('r('.  and  Santiaizo  in  the  Smitlicrn. 

;9.  U\  similar  dliscivations  with  a  Meridian  Circle,  Mars  liein^^  coinpaieil  with  ii  imiMlKd- 
of  pro-soleete(|  stars.  'J'his  is  the  inethdd  pnipd.-ed  l)y  Winneeke,  and  most  extensively  earried 
out  in  ISC.'J.  it  waslirst  employed  in  \s:',-2,  hetween  the  Observatories  of  (Jroenwieh,  Cambridt;;e, 
and  Allnn  1,  in  liie  Nmllieni  Ilend-pln  re,  and  Cape  of  Ciond  Hope  in  the  Snnlhern.  The  residt 
was  1)".(»'JS.*  whieh  il  nnw  appears  was  not  oidy  nearer  the  truth  than  I'lneke's  value,  Init  was 
all'eeted  with  a  prohaldc  error  less  than  tin-  alisojulo  error  of  the  latter. 

As  compared  with  the  lirst,  tiiis  phin  has  this  advanta;:e:  that,  comparisons  lioiiijj,'  mado 
with  the  same  stars  ni,i:ht  altor  iiii;lil,  theic  is  little  dan^'er  of  oliservations  Ix'in;^'  lost  at  oiio 
station  for  want  of  correspondiiiL;-  ones  at  anolhei-;  while,  liv  (he  other,  sinc((  tie.-  planet  must  he. 
compared  with  a  dilferent  .-tar  on  eveiy  iii^ht,  thev  will  be  hwl,  urdess  made  on  the  same  ni^'lit 
at  both  stations.  'J'he  (lisadvanta.i;-es  are,  that  the  residls  are  ailectt'd  l>y  the  errors  arishifi; 
from  crroneoiis  division  ol  the  circle,  or  othi'r  causes  |)ecidiar  to  each  star,  and  t!ial  t\n*  obser- 
vations cannot  be  i-epcaled  on  the  .-ame  ni;^lit.  '!'he  proliable  mauiiitnde  of  the  lirst  error  may 
be  inferred  from  the  results  of  the  investi;.:;ations  of  Auwers  on  the  declinations  of  the  funda- 
mental stars,  from  whi(  h  it  would  seem  that  the  probable  erroi'  ;irisin,n'  frorii  these  causes  is 
between  two  and  three-tenths  of  a  sec(Uid.  it  is,  ther(d'ore.  advisalile  to  compare  with  as  many 
stars  as  jiossilile.  in  older  to  diminish  the  ciiaiices  of  error.  Inaliilily  to  re|)eat  the  observa- 
tions will  ap|>ear  a  less  seri(Uis  objection,  if  we  rellect  that,  from  some  cause  m-  another,  micro- 
metric  comparisons  with  an  Krpiatorial  do  not  often  e.xhioit  the  precision  of  meridian  observations. 

On  the  whole,  1  conceive  that,  in  a  LCeiieral  combination  of  the  [jriiicipal  a(;tive  Observatories 
of  th(>  world,  the  iiiicroiuetric  method  woidd  bi'  preferable;  while,  if  the  number  in  either  lieui- 
isphere  is  limitiMJ  to  one  or  two,  the  preference  must  ii(>  ^iven  to  the  Cin.'le  observations.  The 
;irran,u-einents  of  1862  were  precisidy  the  reverse  of  this. 

y.  By  <'ill'erences  of  Itight  Ascension  between  Mars  and  iiei;j;Iibiu'in^'  stars  east  ami  west  of 
the  Meridian,  .^o  far  as  1  am  aware,  this  method  was  first  employed  by  the  .Messrs.  Bond  at  the 
Observatory  of  Harvard  Colle-i-e,  duriii';  the  opposition  of  lS4t)-50.t  The  value  then  obtained 
was  8".005,  with  a  probable  error  of  0".4.  It  was  also  proposed  by  the  A,-troiiomer  Ko\  al,  and 
actually  employed  at  the  Royal  Observatory,  Greeiiwiidi,  in  I8Gl'.  The  result  has  not,  1 
believe,  been  j)nbiished. 

This  method  has  not  received  the  attention  it  deserves,  probiibiy  from  a  general  distrust 
of  time  observations,  if  employed  at  a  station  of  less  than  forty  decrees  latitude,  with  a  steady 
and  carefully-adjusted  instruumeiit,  ami  if  care  be  taken  to  eliminate  every  source  of  constant 
personal  error,  its  results  mij;ht,  i  conceive,  be  received  with  entire  coniideiiee.  Among  the 
measuies  necessary  to  secure  a  reliable  result  may  be  placed  the  making  of  the  observations  on 
one  side  of  the  uieridiaL  with  an  inverting  eye-piece,  that  the  apparent  direction  of  motion  of 
tiie  jjlanet  may  be  as  nearly  as  possilije  tiie  same  on  both  sides  of  the  meridian. 

It  is  possible  that  observations  over  tiio  horizontal  wires  of  an  Alto/.imuth  might  be  pref- 
erable to  that  over  the  right  ascension  wires  of  an  Equatorial. 

;>.  From  tltc  Observed  ParaUactie  Int'inalUtj  of  tlie  Moon. — This  inecpuility  has  the  solar  parallax 
as  a  factor,  into  which  it  is  multiplied  nearly  fifteen  times.  Since  astronomers  ought  to  be  able 
to  detoruiine  the  coellicient  of  this  inequality  without  a  probable  error  of  more  than  a  tenth  of 
a  second,  the  solar  parallax  ought,  it  would  seem,  to  be  determined  from  it  without  a  probable 
error  exceeding  0".00T,  and,  therefore,  with  greater  precision  than  by  any  other  method  yet 
employed.  Unfortunately,  however,  the  uncertainty  of  the  observed  value  of  the  parallactic 
inequality  still  amounts  to  several  tenths  of  a  second,  so  that  there  is  no  hope  of  attaining  this 
degree  of  precision. 


\. 


*  Abtiononiische  Nuchrithteu,  No.  'lij'i. 


t  Astronomical  Journal,  No.  lOU. 


MMfe4«<U.U.JJli ''-""."-««'"'■"* 


k. 


ANJ)    rilK    KI.KMHN'I'S    WHICH    DKIMlN'lt    ll'ON    11'. 


;{ 


\. 


'I.  Hjl  (■tiiiiliiiiliKi  till  Ijiiiiiir  Jilt  ipiiilih/  ill  II, r  Mnliihi  III'  lliv  /','iiiili  iri'li  tin  kimirii  Miisn  n/'  lln 
Mm, II.  —  IJy  this  iiu'tliiid  Wiis  (ilitiiiiiiMl  tlit'  Viiliic  of  the  s(i|;ir  piiralhix  a(l(i|>lcil  li\  |jt>  N'cnicr  in 
liis  soliir  tallies.  KikiwIhi^-  tlic  paialliix  and  mass  oi'  tin-  Monu,  wc  can  (•(ini|iut('  liic  ili-^lamc  ol' 
till'  (H'Mtro  of  tlic  Earth  I'roiii  tiic  (•nniin(ni  centre  ol' ij;iMvit_v  of  the  Kaith  ami  Mnun,  amnml  which 
tho  Kivrth'rt  cenfre  revolves  in  ii  lunar  nnmth.  Also,  from  ohservations  of  the  Sun,  Venus,  or 
Mars,  wo  can  determine  the  aULjle  which  this  sanu'  distani'c  sul>tends  when  seen  IVoni  the  Sun. 
A  eomparison  of  IJMse  two  data  j,iives  the  an^le  wliich  the  I'adins  of  the  I'larlh  it>e||'  suhlends, 
as  seen  rroiii  tho  Sun,  (.r  the  solar  parallax. 

This  method  is  tlu;  least  precise  of  all,  since"  it  jiivcs  (he  solar  parallax  as  the  |iro(luct  oi' 
two  factors,  noitlicM'  of  which  are  determined  with  ;j;i>  at  precision.  The  observed  value  of  the 
lunar  eijuatioii  must  at  present  (h'pend  on  oliserveil  ri;4'hl  ascensions  of  the  Sun,  of  whicli  the 
probalilo  error  is  very  laij:e,  and  tiie  uncertain  factor  of  this  element  is  ahoiit  one-third  ;^reater 
than  unity.  Therefore,  snpposiii},;  the  mass  of  the  Moon  known,  the  uioi'c  lo;j,ical  course  would 
seem  to  lie  to  determine  the  lunar  inecpiality  from  the  solar  parallax. 

.').  Fruiii  Kr/icrliiK  iilid  I)i  hriiiiiinliii/iN  ii/'  tin  Vi-lniihi  of  Llijlil,  rmiiliiiinl  irilli  tin  l:iiiiini  nilur 
of  llic  All'  rniliiiH  III'  fjiijlit. — Foueault's  lieautifid  experiments  with  the  revolving-  mirror  art!  so 
well  known  that  tln'v  need  not  he  descrilied,  'I'lie  theoietical  olijections  to  this  method  do  not 
seem  to  mo  to  have  much  toic(>,  and  1  se(>  no  iusuperahle  reason  why  its  results  should  not  he 
US  reliable  as  thos(!  of  any  other  method.  It  is  (piite  true  that  in  experiments  so  delicate^ 
hidden  causes  of  constant  error  may  defy  the  scrutiny  of  the  experimentalist.  It  is  also  true 
that  Foucalt's  operations  liav(>  not  been  published  with  that  fullness  of  <|etail  necessary  to  satisfy 
astronomers  that  his  results  could  not  have  been  vitiated  by  any  smdi  cau>(!.  I5ut,  to  test  the  reli- 
ableness of  lii(!  results,  it  is,  1  think,  oidyjiei'essary  that  the  determination  should  be  repeated  with 
apparatus  a.s  dilVeriuit  as  possible  from  that  used  by  Foucault.  Such  a  rep.'tition  is  a  desideratum 
bothfor  Physics  and  Astronomy.  A  desirable  modi  Heat  ion  of  tho  apparatus  would  ln',  if  practicable- 
placing  tho  fixed  refiector  at  a  gr(.'at  distance,  say  ."{.OOO  or  4,000  metres  from  the  revolving  mirror. 

When  the  Great  'J'ransit  Ciicle  was  mounted  at  tin;  Naval  Ohsei-valoiy,  the  (pH>stion 
arose  whether,  in  the  reduction  of  observations  of  the  Sun  and  I'lanets,  it  ,\as  jiossible  to 
eiriploy  a  value  of  tin?  parallax  so  near  the  triitii  that  there  would  be  little  (h.nger  of  future 
investigators  having  to  cdrrect  our  results  on  account  of  eri'or  in  tlie  adopted  constant  of  s.ilar 
parulhix.  The  most  proi.dsing  source  of  an  accurate  parallax  seemed  to  be  the  observations  of 
Mars,  made  in  18(!2on  tho  plan  of  Winneeke.  'I'hey  formeil  a  better  planned,  better  executed, 
and  more  extended  series  than  was  ev(M-  b(d'ore  available.  In  tin,'  Southern  iJeunsphere  the 
Observatories  of  Williamstown.  Cape  of  Good  llopi-,  and  Santiagt..  .vorkeilwith  remarkable  suc- 
cess, securing,  altogether,  observations  of  Mars  and  comparison  stars  on  14.'!  niiihts.  In  tlio 
Northern  I-Ieii)isph(!re  the  Observatories  of  Pulkowa.  I'eterslmrg,  llelsingfors,  \'ienna.  Berlin, 
Leiden,  Greenwich,  Albiiny,  and  Washington,  ar(>  known  to  have  co-operated.  So  extended 
ii  co-operative  eilbrt  on  the  part  of  astronomers  all  over  tho  civilized  world  has  not,  I  believe, 
been  seen  since  the  transit  of  Venus  in  tho  last  century. 

Throe  partial  discussions  of  these  observations  have  appeared. 

1.  Winnocke,  by  a  comparison  of  observations  at  Pulkowa  and  tho  Cape  of  Good  n>)[)e, 
on  thirteen  corresponding  nights,  found  tho  solar  parallax  S". 9(i4.* 

%.  Mr.  E    J.   Stone,  of  the   Royal   Observatory,  Greenwich,  discussed  tho  observations  of 
Greenwich,  the  Cape,  and  Williamstown,  deducing  the  parrallax  8".it43.+ 

3.   The  corresfionding  observations  at  Albany,  Washington,  and  Santiago,  were  discussed  by 
Mr.  Ferguson  in  the  Washington  Astronomical  Observations  for  ISO.''!,  with  the  following  results: 
From  12  oliHcrvations  of  W;isliingt()ii  aiul  Santiago  -     -     -     -     8".8,'M 
\h         "  "     Albany S'.Gll 


Astrononiischc  Niiclukhten,  No.  14t'!). 


t  Memoirs  of  ttie  Royal  Astioiioiiiical  Society,  Vol.  'X\,  p.  97. 


4 


INVKHTKiAl'ION    OK    I'lli:    DISTANCK    <)1'    TIIK    «UN 


The  nictliod  !i(l(.|)t<'(l  by  ciicli  ..!'  tlii'so  iiivr>ti;riit.)rs  Wiis  fliiil  (if  (•(Uiiim 'ismi  (if  piiirs  of 
(•(irics|iniiiliii).'-  (iliscivatloiis  iiiinli'— (UK-  ill  ciicli  licinisiilicrc.  Miiiiv  uliscrviif iniiK  iit  tlic  niui 
Htulioii  wiiiilil  lie  lust  Wiv  uiiiil  iif  cirii'siioiHliiij;  <ili>civati(iiis  at  tin'  dllicr.  Thus,  mit  oi  ii  ^M'aiwl 
Intal  (if  iiK.ri'  than  ;!(»()  iilir-cival ions,  (inly  2<)  wtic  ('iii|il(iy('(l  liy  WiiiiHM'k(\  TiH  by  Stone,  ami 
K;  by  Fciyiisoii.      l-'ivc  of   tliosc   used  by  Winn,  rkc  aid   Stoiio   bcinn-  tlic  Humo,  tlic  ^iiiii  total 

ii.mmI  iiy  flic  tlircc  asti( incrs  is  only  I'J').      Tlic  lliicc   results  arc,  tlicroforo,  so  far  from   liinil 

thai  a  ('oiii|il('t('  (lisciissioii  is  to  lie  dt'sircd. 

'i'liis  discussion  I  have  iu-eii  |MTiiiil  tc(l  and  cnaldci!  to  nndci'takc  by  Rear- Adiniial  Chark^s 
11.  I»avis.  lat(dy  Sii|.ciiiitendciit  of  thn  Naval  Obscivatoi*'.  At  liis  re(|Uest,  copies  of  the  iin- 
imblishcil  (.liservalions  of  Williainstown  and  the  Cape  \vcr((  obtiiincd  from  Robert  .1.  lOllery, 
es.]..  and  ^-ir  Thomas  Maclear,  the  directors  of  those  Obscrvat.nies.  The  Observatory  of  Tnl- 
kowi,  as  the  orijiinator  of  the  plan,  haviiif;'  u  jnior  rijiht  to  the  .general  discussion,  its  consent 
was  also  obtained  thronuh  its  (list in;;nislied  director,  who  coiiiiminiciited  the  obs(jrvations  ol 
Sawitch  and  Kreii^'er.  made  at   l'etersl)iir;;'  and  llclsini^fors. 

The  IdllowinL;'  coiisideratiiais  may  lead  to  a  method  of  deterininini;-  the  parallax  of  Mars 
from  observalions,  inoi'c  sinipit!  and  ri^'orous  than  that  of  correspond  in-'  jmirs  of  obsorvatioiis: 
'I'he  perturbations  iiitiic  motions  of  the  Earth  and  Mars  lu'ine;  perfectly  known  for  the  period 
which  we  consider,  every  observation  of  that  planet  will  lead  rigorously  to  an  iMpiation  of  con- 
dition iiclv  cell  its  parallax,  the  six  elements  of  its  orbit,  and  the  six  (dements  of  the  Karth's 
(libit,  'I  hiileen  or  more  observations  will,  when  compared  with  any  theory,  snilice,  formally, 
to  correct  the  elcmeiils  (d  that  theory.  But,  if  the  observations  extcMid  throu(;h  only  a  short 
interval,  say  one  month,  the  coellicieiils  ol'the  corrections  will  be  so  miniitt!  that  no  trustworthy 
values  i\[  the  corriM'tions  can  be  deduced.  We  shall,  in  fact,  lind  that  our  e(piations  will  only 
snilice  to  determine  a  lew  functions  ol'the  elements,  and  that  the  (dements  themselves,  if  their 
values  are  only  chosen  so  as  to  satisfy  those  I'unctions,  may  all  vary  widely,  without  ceasiiin'  to 
satisfy  our  cMpiations  of  condition.  If,  now,  we  can  lix  a  priori  f)n  the  entire  number  of  functioiKs 
of  this  kind,  and- use  them  in  litiii  of  the  elements  of  the  Earth  and  .Nbirs,  our  ("(juations  will  be 
practically  as  rigorous  as  il  we  had  introduced  the  entire  number  of  thirteen  unknown  (piantitiei-. 

One  of  these  functions,  the  lirst  one,  indeed,  will  be  the  error  of  declination  of  Mars,  since 
this  will  be  f;iveu  by  a  single  pair  of  observations.  Rut,  when  there  are  a  series  of  observa- 
tions, we  mav  takt',  instead  ol'  the  declination,  the  absolute  distance  of  tlie  planet  from  tlio 
l.lane  of  the  Earth's  ecpialor.  This  distance,  or  rather  its  error,  may  be  developed  in  power.s 
of  the  time,  and  the  coellicients  of  this  development  may  be  taken  in  lieu  of  the  elements. 
That  is,  we  \u:\\  assume  that  the  error  of  tabular  decdinatioii  may  be  expressed  in  the  form 

st'f  Dec.  ,        .  I        ,    , 

That  this  assumption  is  a  safe  one  in  the  case  of  Mars,  may  be  shown  by  takinp:  the  ob- 
st'rved  tabular  iirrors  i;iven  by  Winneeke  in  his  publication,  '■  Ikobacht'ingeii  des  Mars  um  die 
zeit  der  Opposition,  U^d'J,"  and  developin;;'  them  in  this  way.  Dividing-  them  into  five  series,  and 
taking-  the  mean  oi'  each  series  as  the  error  corresponding  to  the  mean  of  the  dates,  wo  have 
the  ibllowing  live   tabular  errors,  and  their   products  by  the  distaiico  of  Mars  from  the  Earth: 


' 

—- 

.... 

Unt 

i'. 

e 

f  XA 

Ol.s. 

Aiifr. 

:n 

4.  !2H 

I.0(> 

.-, 

Sept. 

17 

.5.  r>H 

•i.  10 

11 

lid 

.f-..  1!) 

:;'.  II 

7 

Oct. 

14 

4.  .v. 

].i>4 

J 

1 

M 

:i.  Wi 

i.7:i 

•> 

^ 


._....^  <;r 


AND   TIIK    KLKMKHTH    Wllini    DKI'I'.ND    I'I'oN    IT.  6 

Dovi'lopiiiiJ,'  till'  lust  I'dliiiim  ill  |)(i\V(<rs  nl'llir  time,  ami  rcliiiiiiiiu-  nnly  liiifi'  I.Tin-*,  we  sliali 
find  tliiil  iiiiiu'  (if  till'  (li'viiitidiin  lidiii  the  Idriiiiilii  \\ill  aiiniiiiit  to  0".  10.  'I'lio  cticHificiit  of  llm 
Hecond  luiwur  of  tlu)  tiiiiu  Ixiiiii;  only  0".00(»;}.'),  it  iimy,  I'ur  a  pt'ritnl  of  ti'ji  days  on  iMidi  sidu  of 
any  opo(di,  l>o  iicjilcctcd  witlmut  daiigiT  of  crrnr. 

It  is  to  bo  rciiiarlxi'd  that,  lii'sidcs  tliosi!  tiTiiis  dividcil  liy  J  in  tin-  i-xprrssioii  for  I'lror  of 
tubular  docliiiatiuii,  tlicro  may  bo  a  {'oiistaiit  toriii  arisin;;-  from  constant  soiircos  oj  error  in  llic 
inoawurod  polar  dirttaiiceH.  I'littiiij:;  J'= -Jcos  Dec  and  «ff=oi)n'ootion  of  paiullax,  oacli  com- 
parison of  an  obsorvo(|  and  compiitoil  docliiiatioii  will  ii,ivo  an  (Mpiatioii  ol' the  lorm 

'J"i   'V  «•  ""''  /^  boin^'  tlio  unknown  (jiiantitios  to  bo  dotormiiu!il. 

S  J. 
Tlio  followiuj;-  is  tlio  list  of  observations  included  in  the  (bsiaission,  with   tlio  aiitliorit  ios 
for  tliom : 

NOUTIIKHN   OliSKItVAIOKMES. 

Pull-owa. — Tliii'ly-oiie  obsorvatioiis.      Ho()baclituii;^("i  dos  Mars  von  l»r.   A.   \Viinn'cko. 

i/c/,su(r//or.s.— Eiglitoen  observations.  Beobaclitmi-'on  dos  Mars  nnd  dor  Winnockosolion 
Vergloichsteriie.  Horhst,  1802,  am  Roiola  idiach-HrtoIsclion  Moridiankroiso  dor  Storiiwarlo 
zu  lIolsiii<i,'lbrs.      (Coiiiniunioiited  by  M.  Strnvo.; 

Lcidni. — Twenty-niiio  observations.      Astronoimsclio  Niichrieliteii,  IJaiid  (!2. 

Greenwich. — Fourteen  observations.      Ci'-i'mwioli  Observations  of  ISIi'i. 

AJhany. — Twenty-six  observations.     V      Jiington  Ol's^i v.itions  ol    ISO.''.,  p.  xi.ix. 
U  ashimjlon. — Thirty-six  o\iHervations.      Wa^li,  i^ton  Observations  of  I8()2. 

SOUTHERN   OI!!-r,KVA'l'()RIES. 

lyUUfunstoivn, — Fifty-ono  ob.servations.      Resid;    coinmunieiit(;d   by  iJobort  .1.   lOUory,  esi|. 

Cape  of  Good  Hope. — Forty-thvoo  observations.  Obsorvati.ins.  with  their  rediietions,  com- 
municated by  Sir  Thomas  Muclear. 

Surdiaijo. — Forty-nine  observations.  Observaciones  Moiidiana'.  i  Micr(m>otricas  rolativas 
al  Planeta  Marte  al  Tiempo  de  su  oposiciou  en  18()2,  voriiiradas  en  el  Observatui'io  Nacional  do 
Santiago  do  Chile.      Santiago,  IBO."^.. 

This  includes  the  entire  list  of  those  accessible  observations  the  weight  of  which  would 
be  such  as  to  sensibly  afTect  the  concluded  'j^arallax.      The  entire  number  is  as  follows; 

In  the  Northern  lleinisphei-" 1  "i  I 

In  the  Southern  Hemisphere 143 

Total 2!)7 

In  discussing  the  observations,  the  first  thiir^  to  be  (bine  is  to  make  thorn  .-strictly  com- 
parable with  each  other.  This  is  eflected  by  dedti';iiig  them  all  dinerentially  from  one  set  of 
comparison  stars.  In  Winneeke's  plan,  each  observaMon  of  Mars  can  be  compared  with  similar 
observations  of  eight  stars  of  comparison.  An  epheineris  of  the  positicjiis  of  these  stars  being 
prepared,  a  comparison  of  the  observed  polar  distance  of  any  star  with  the  ephenu'ris  gives  an 
apparent  correction  to  the  observation.  The  mean  of  th'^  eight  corrections  thus  deduced  from 
one  night's  work,  by  one  observer,  is  considered  a  eorrectj.on  applicable  to  the  polar  distance 
of  Mars,  observed  on  the  same  evening. 

If  every  observer  observed  all  eight  comparison  stars  on  every  night,  the  ado[)ted  moan 
position  of  each  star  would  be  a  matter  of  entire  indill'orence.     But,  .since  a  portion  of  the  com- 


^  < 


6  INVEfSTIGATlON    OV    TIIK    IHSTANCK    OF     I'lIK    SUN 

|)iiris()ii  sliu-M  wi-vc  iVcciiiontly  misled,  it  liccomcs  iiaporlaiif  that  the  .lilVoront  stars  should  bo 
rcMluccd  t(.  tin-  same  staiulanl.  Ki,-or..nsly,  tliis  slamlanl  shouM  ho,  not  that  of  al.sohito  correot- 
noss.  hilt  that  of  each  particuhu-  iii>trnin(Mit  as  allV,i.-,l  with  its  errors  of  divisions,  and  corrected 
for  the  constant  error  of  the.  mean  of  its  positions  of  all  ei-ht  stars.  This  standard  being 
unattainable  for  want  of  a  snflicient  number  ol  obsiMvations,  we  shall  be  obliged  to  use  one 
uniform  set  of  star  t'laces,  dilVering  IVom  absolute  truth  by  amounts  less  than  the  accidental 
ernu-s  of  division  of' our  instruments.  The  adopted  positions  will  be  derived  from  the  obser- 
vations of  (Ireenwi-h,  Pulkowa,  Albany,  and  Washington.  The  adopted  standard  of  dei'lination 
will  be  that  of  Auwers,  in  his  paper  on  the  corrections  neces-^ary  to  reduce  the  diiVereut  cata- 
logues to  a  fun<lamental  system.  This  veducti(Ui  will  be  obtained  through  t!ie  Greenwich 
Transit  Circle,  the  cirrection  of  which,  near  the  K.piator  is  -}-()".  2.  Comparing  !lie  observa- 
tions of  I'ulkowa,  \Vasliii:gton,  am!  Albany  with  those  of  (Greenwich,  thus  corrected,  we  lind 
the  following-  svsteiiiatic  corrections  to  reduce  them  to  Auwers: 


J'ldkowa 
Albany  - 
^Vaphiiiirteii 


+  ].:■ 

—  i.r, 


The  mean  decliuiitions  ibr  1S(;2.().  thus  concluded  from  the  observations  of  each  Observatory, 
with  the  seconds  >A  coiiehided  north  polar  distance  for  the  same  eiiocli.  are  given  in  Table  I. 
The  po>itions  under  the  nauK^s  of  the  Observatories  are  not  corrected  for  systematic  enor. 
The  small  hgures  after  each  '-esult  show  the  number  of  observatii-ns.  The  weights  are  not 
proportional  to  the  numl>er  of  observations,  but  on  a  somewhat  arbitrary  scale,  depending  on 
the  proiiable  errors  of  divisions,  and  the  discordance  of  individu.il  observations  at  the  several 
Observatorii's.  In  'J'able  11  is  given  an  ephenieris  of  apparent  positions,  computed  \vith  the 
conslanls  of  the  American  Ephemcris  and  Nautical  Almanac. 


41 

(iO 


;  120 

j  2(1 

'  HO 

■  Sit 

4:5 


l,!il;iii(lc  47:i74 
LiiliMidc  'Jt!l  . 
I'isciiiiii  .  . 
I.mI.'iikIi'  (iTO  . 
Ccti  .  .  .  . 
I'isi'iuni  .  . 
l.iihmde  I'init. 
I'isciniii  .  . 
Ccti  .  .  .  . 
(Vti  .  .  .  . 
(Vti  .  .  .  . 
I'isciuni  .  . 
I'isciuiii  .  . 
(*cti  .  .  .  . 
I,;il!in(lc'i<;i4  . 
I'isciuiii  .  . 
I'isciuiii  .  . 
Liilaiidc  ;W!18  . 
I'isciinii       .     . 


TAIil.K  1. 

i 

c 

> 

O 

S 

r. 

< 

—  ;} 

l!t 

4.5.1     u 

4.i.l 

•1 

4:!.4    8 

" 

-  0 

.'i,") 

l.'j.d    (i 

;(.-.s 

f< 

I7.!t  1,-, 

i.'i.S    ;! 

'_ 

-  1 

10 

yit.4  (i 

;;i.o 

7 

;n.!i  r, 

•  yi'.'J      H 

_ 

-  4 

5 

4r)..'>  M 

4t!.8 

5 

48.:?  oo 

4.-).l   lit 

—  1 

1.") 

47.0  11 

47.0 

:i 

44.7  10 

48.1     7 

'_ 

r-  r^ 

;■)!• 

V2.1    c 

\->A 

o 

14.8    (i 

11.7    ;i 

_ 

^  4 

:il 

Vi.7    ■.' 

14.0 

,') 

14.8  III 

.         , 

_ 

-  (i 

4!> 

5^.8     Ml 

.5!  (.7 

It 

(;i.8   1,-, 

.W..-)    IS 

—    1 

.••).•! 

40.(1  17 

.•i!».5 

H 

.18.7  :ii 

40.!l  ai 

J 

-  0 

:i7 

;w.7  ic 

;u.!t 

ir. 

'MA  -M 

;W.t)  a.'i 

-  1 

n; 

14.-J    a 

\r,.2 

8 

1().8   10 

. 

_ 

-  4 

.').-) 

'^.•^  J  4 

(1.8 

.'> 

•t.l    Ift 

(i.O  ir, 

_ 

_  •) 

.>{ 

il.Q  11 

V>.'2 

8 

14.0  11 

11.0     1 

1 

—  1 

10 

•Jl.(i    10 

'21.8 

1 

1!>.7  II 

'     '."i.S    fi 

—  1 

(1 

()■».:{   B 

()'->..'-. 

4 

.');i.7    ti 

( ;•>.(;  a 

-  5 

'2"> 

.')1.(!  ifi 

.'SI. It 

7 

'M)  li) 

r^o.-i  8 

_ 

-  4 

.(T 

I.Vi  in 

Kl.'i 

i:i 

18.4  1", 

14.8   Hi 

-  i 

.-n* 

4*i.O  10 

v.u 

7 

4.'5.0  in 

41. 'J  i:t 

- 

_  ') 

;{0 

KU!  10 

17.7 

" 

i     1!M!  ir. 

l(i.:i  1.-. 

!^w" 


"Cm 


44.15 
4:{.'21 

'2!  •.:{'> 
l:{.'24 
Ki.Oli 
4(1.75 
4(  ;.:?'> 
5!).8!t 

•.i'.ir,:] 
25.00 
44.(i4 
53.48 
47.(17 

ao.7(; 

!.:!'* 

7.50 
4:1.45 

1(1.80 
42.08 


\. 


AND    TII,K    KLKMKNTS    WlllCir    DKI'KND    UPON    IT. 

TABLK  II. 

Ep/u'iiirn's  (if  (lie  appaidd  Xorlh  PaJar  (Ustiuurx  /or  (rcaisit  over  (lie  )ii<i!(li(ni  <>/  IVas/iiiKflnn. 


s. 


Mr 


n 


J.X 


I'll, 

ST  SKKMK 

-0  I'is. 

II  I'is. 

r  I'is. 

4:!29-. 

;  1 

Date. 

.5  I'is. 

•Jii  C'fli. 

••'<!( 'uti. 

is. 

AlliJ.  -iO 

I!.-..  -J.^ 

I2.f^(i 

59.  22 

2^1.  (II! 

4:i.  -'(> 

211.(1(1 

,5:t.  IS 

H 

5S 

:!(• 

:i:i.  ss 

1 1 .  "^7 

5s.  i:( 

211. 7C> 

42.  .59 

l-'.s:i 

.52.(12 

17 

44 

Sci)t.    '.1 

;!'J.  c.) 

II.  17 

57. 21^ 

25. 7 1 

4 1 .  55 

17.-*:! 

51.  12 

1(1 

."l.'» 

l'.> 

;ii.77 

111.74 

5(1.  7(t 

24.91 

41'.  7:! 

17.  (17 

5(1.  15 

15 

94 

29 

ai.MC, 

m.  ,55 

.5(1.  :i7 

24. ;!;! 

III.  It; 

1(1.  55 

5(1.(15 

15 

54 

SECOND  i^EKI 

KS. 

-9  I'is. 

I.ul.  2(114. 

,"  I 

Datr. 

Liil.  (17(1. 

15  Ccti, 

11(1  I'is. 

1 
20  Ccti. 

4:iCi'ii. 

is. 

^, 

^, 

1 
1 

H 

^, 

,, 

^, 

Sipt.  19 

44.4:5 

17. (Mi 

M.  47 

11.  (iC. 

2(1.(14 

.52.  79 

:!:i..5(i 

4(1 

/  5 

29 

4:».  H(i 

Ki.Sli 

17.^^0 

Id.  ;>ii 

19.(111 

.52.(1(1 

:i:t.  lid 

Id 

111 

Oct.      9 

4:i.  54 

Ki.Sli 

17.  :!s 

9.  97 

19.4(1 

.52.(11 

;i;!.  ;t(i 

;!9 

-1 

TiiiKi)  sKini:."^. 


Dat.'.     iLal.  2fil.  :     44  Pis.       Lai.  C70.       15  Ccti.        2(!  C.ti.        Hi  Pis.         ,"'9  Pis.         4:!  Ci'ti. 


Oct.      9 

i:!.52 

59.  7:5 

4:t.  54 

Kl.  K! 

.5(1. 29 

2:5.  99 

19.40 

.52.(11 

19 

i:{..5H 

.59.  78 

4:5  4:5 

17.04 

5(1.  44 

2:5.  sf, 

19.41 

.52.  92 

29 

1:5.88 

t)U.  08 

4:1. 50 

17.47 

5(1.  74 

2:5.  92 

19.(14 
2(1  Ceti. 

5:5.  42 

FOI 

JKTII  Si: 
Liil.  1170. 

{IKS. 
Lai.  1299. 

20  Ceti. 

Date. 

L.  437:54. 

Lal.atil. 

44  Pi.s. 

29  Cell. 

Oct.    19 

15.  If) 

1:5.58 

.59.  78            4:5.  4:! 

17.82 

10.89 

.5(1.  44 

1(1.45 

W 

1.5.  (i2 

1:5.82 

(10.01      1       4:i.  5(1 

17.95 

ll.:tl 

.5(1.  74 

1(1.7(1 

Nov.    ti 

16.21 

14.22 

ti0.40     I       4:1.74 

i 

18.  19 

11.92 

57.21 

17.20 

The  observations  being  till  reduced  according  to  one  iiiiit'orin  .system,  no  details  need  lie 
given  except  tor  tliose  cases  in  wliich  a  mode  of  observation  dilVerent  from  that  WinneeUe  lias 
adopted,  or  in  wliich  some  of  the  elements  of  reduction  are  doubtful  or  imjierfect. 


GiiKi:.N\vicii. 

Only  a  small  number  of  the  comparison  stars,  seldom  more  than  four,  were  observed  on 
an\'  one  evening.  Tvloreover,  the  same  stars  were  frecinently  sel(M"t(.'d  night  after  night,  so  that 
the  positions  of  Mars  depend  mainly  on  less  than  half  the  entire  list  of  stars.  Tin;  doiilile  wire 
system  was  not  used,  but  the  single  wire  was  placed  alternately  tangent  to  the  two  limbs  of 
the  planet.  P^'oru  the  discordance  of  the  measured  diameter.-,  this  method  would  appear  inncli 
leas  accurate  than  that  of  double  wires. 


8  IWKSTKJATION    OV    TIIK    DISTANCK    OK     I'lIK    SUN 

A  i,i;a\v. 

Ilcrc!,  also,  ii  siiiulc  wire  was  placiM)  nltiM-Miitcly  taiiu'i'iit  to  tlio  two  liint)s  of  tlio  pliUiot, 
several  contacts  witli  each  liinli  lieiiiu-  iiiaile.  As  tlie  fixeil  wire  was  used  in  tlioso  !iieasnrcs, 
and  lliere  wa>  nut  time  to  read  tlie  mici:isco|)es  lur  all  the  contacts,  tlie  leatlinj^fs  were  rol'erred 
to  tiie  n)icidsc(i|ies  liy  an  a|i|iaratiis  invented  !iv  Mitciiell,  called  a  Declinometer.  Tiiirf  appa- 
ratus is  descrilieil  in  tin'  puMication.-  el  tlie  Dudley  Ohservatoiy,  and  the  mode  of  usiiiu;  it  in 
tiic  present  ease,  as  well  as  an  aiistract  of  the  oiiservations,  maybe  found  in  tiie  volume  of 
Washington  ()liservatinii>  for  Is(!;>.  Owiii;:;  to  the  irren'iilarity  of  this  nietiiod.  I  have  hesitated 
til  admit  its  results.  IJiii  alter  a  carcinl  scrutiny  of  the  observations,  and  a  piM'sonal  i-xamina- 
tiiin  of  tlie  apparatus,  1  am  iinalile  to  see  liow  any  sourci'  of  constant  error  conld  have  cri'pt  in, 
and  have  therefore  admitled  them  with  a  small  wci ,;ht. 

WASIlINCTiiN. 

During;  the  first  series  (until  September  21)  the  stiir  observations  were  irregular,  two  of 
the  observers  |dacin:^'  the  star  ima,:;c  between  the  wires,  and  tlio  third  usiiijj,-  wire  1  exi'hisively. 
The  employment  111  the  foriiier  system  for  a  limited  number  of  the  obs(>rvations  does  not  seem 
l<i  be  iibjectiniialile.  siiKc  the  constant  errors  to  which  it  is  known  to  be  liable  may  eiiually 
alfecl  liiseclimis  of  a  star  by  a  wire.  I>ut  when  the  same  wire  is  used  for  all  the  ci)m[)arisou 
star^,  and  the  mean  of  the  two  wires  for  Mars,  any  error  in  the  ado|)te(l  distance  of  the  wires 
will  all'ei't  all  tiie  oiiscrvat i<ins  in  the  same  way.  This  distance  bi'inj;'  determined  from  nadir 
<d)scrvations,  in  tiie  manner  described  in  Washin^^lon  Observations  tor  ISOo,  p.  XXVll,  doCvS  not 
se(\n  rclialile.      It  was  tlicrcd'orc  redi'termined  in  the  followiii!:,'  way  : 

I.  Heference  was  made  to  tln'  original  oiiservations  for  nadir  point  in  l.Sfi-,  and  every 
result,  both  tor  single  and  double  iiiti'i'val  ol  wires  durinj^  the  entiix-  soriiis  of  parallax  obser- 
vations,  was  classified  accordin;^"  to  the  observer,  and  ariMU^ed  in  the  order  of  time. 

These  results,  beiiii;'  supposed  afl'ected  only  with  constant  personal  errors,  p;ave  entirely 
reliable  values  of  the  cluutijin  of  distance  at  tliosi;  epochs  when  the  wires  wire  disturbed,  though 
none  of  the  al)solute  distanci's  are  con^ideri'd  reliable.  It  was  thus  found  that  tiie  distaueo  of 
the  wires  from  Scptemlier  -I  to  October  '1  was  greater  by  Or.  GOTO,  or  ()".4"),  than  from  October 
7  to  November. 

'1.  'I'lic  absnluti'  distance  from  October  7  to  November  was  derived  from  observations  of 
couples  of  stars  made  tin  couples  of  dates,  on  which  the  order  of  use  of  wires  was  revinsed. 
Let  D,  and  Do  be  the  declinations  of  a  star  (U'diiced  from  observations  on  two  dates  with  wire.s 
I  and  "J,  re>|iecliv(dy ;  ii,  and  d^  the  declinations  of  another  star,  deduceil  on  the  same  dates  with 
wires  2  and  1.      Then,  it   h  be  the  correction  to  the  adopted  distance  of  wires_  we  shall  hav(^ — ■ 

.;=i(D|-D,  +  </,-(/,)- 
Thus  was  found,  i)  =  —  [)".  WVl. 

II 
Adopted  (listfuicc,  ( )ctober  7  to  NovonibiT l.'t.dS 

'I'nic  (iistaiK'i' J^.i)') 

("orrci'lioii  for  ScpteiidK-r 4    "•!•'> 

'J'riie  (bslaiicc  for  Se|itiinber 14.00 

Adopted  distanci'  in  imlilislied  reductions 11.02 

J'-rror  of  pulilislicd  reductions 0.02 

The  correction  on  account  of  ermneous  half  distaiioe,  being  imly  a  liundredth  of  a  second, 
has  been  iiegU'cti'd. 

WlI.I.IAMSTOWX. 

It  is  not  stated  by  Mr.   Kllery  whether  a  single  wire  or  a  pair  of  wires  was  used. 
The   North   I'olar  Distances,  as  forwarded  in  nninuscript,  were  not  corrected  for  errors  of 
divisii>n.     They  were,  however,  aceompaiiiod  by  u  table,  giving  the  errors  of  iliviuion  for  every 


AND    TIIK    KLHMENT.S    WMICII    DKI'KN'I)    IU'()\    11'. 


!» 


(lojrroo  of  zeiiitli  distaiioo.  Uiifortniiiitcly,  it  was  nut  stati'il  (Mtlicr  in  wliat  ijircctioii  tlin  /.(Miitli 
distance  was  coiinteil,  or  wlictluM'  tiui  coiTccf ion  was  to  lie  a|(|ilii'il  to  tin-  ciri'lc  irailinLT,  wliicli 
iniji'iit  increase  toward  tin;  north,  or  tiic  polar  distance,  wliicli  increased  tuw.ard  the  soutli.  In 
this  dilliculty,  recourse  was  had  to  tin'  paper  ol  .Mr.  .'^tone,  who  inin'ht  ii'  snppo-^cd  a<'i|nainlci| 
with  the  facts,  and  who  [xibiishi-d  a  siniii  ir  talilc  foi'  every  10  .  It  Wiis  foiiinl  tliat  he  comili'd 
the  /.enitii  distance  toward  tiic  norlh,  and  apphed  i  lie  correction-;  in  the  suae  direction.  To 
ascertain  whether  tiie  corrections  thus  applied  were  real,  thi;  corrections  t  >  the  adopt(M|  |)hiees 
of  the  stars  were  deduced  frcan  all  the  Williamsldwn  eli>ervations,  without  applynii;'  n-rois  of 
division,  and  then  the  coi'rections  were  corrected  for  errors  (d  division,  in  order  to  sec  whether 
they  were  thus  diminished.      The  ri'sults  W(!re: 


Scrii'S. 


Slim  of  c'oni'ctioiis  luu'oncclcil 
Sum  of  cont'clidiis  corn'i'tcil     . 
Siiiii  i>(  s((iiiii'cs  iiiK'orrci'tuil 
Sum  of  sciuiires  convctcd    - 


II.  III.  IV.  Sum. 


— 



•,'.  '.1 

;!.? 

:!.  '.I 

i:!.7 

.  i     1. 1 

•■>.  .'> 

l.s 

•2.  '.I 

K.-.i 

.  ;     1.-^;! 

'i.  II 

■J. :'.:( 

l.'.H 

■■'.  •') 

a.-J7 

0.  '.»."> 

li.Tl) 

1.:!: 

:!.  •-; 

The  imi)rovemeiit  is  so  well  marked,  tl.e  pruliaMe  error  liein-'  re  liie  d  from  O"..'!!)  to  ()".'J1, 
that  the  correctness  of  the  assumption  can  haidly  lie  doiiiited.  The  errors  of  division  havt; 
therefore  been  thus  applied. 

SANTI.\f;o. 

The  observations  appear  to  have  been  carefidly  made  throIl^•hollt.  Tlnsy  do  not,  howevi^r, 
imjiress  one  with  a  hii;'h  sense  of  the  cxcelleiici'  of  the  .Meridian  Circle,  or,  at  least,  of  the  pre- 
cision with  wdiieh  its  microscopes  can  be  read.  There  is  also  a  weak  point  in  one  of  the  im- 
portant elements  of  reduction,  .namely,  the  inclination  of  the  declination  wires.  Thei'e  ■•ivc. 
two  of  these  wires,  one  fixed,  the  other  movable  by  a  micrometer  screw.  In  the  .Mars  obser- 
vations, the  latter  was  set  over  or  under  tiie  fixed  wire,  at  a  distance  somewhat  less  than  the 
diameter  of  Mars,  and  the  observations  were  then  made  in  strict  accordance  with  Winm^cke's 
pro.uramme.  The  oidy  information  respecting  the  inclination  of  the  wires  is  in  the  following- 
words: 

"En  el  campo  de  vision  del  anteojo  del  Circulo  Meridiano  esta  esteiidido  iin  hijo  (ijo 
paralelo  al  camino  que  recorra  una  estrelhi  ecuatorial.  *  *  *  Por  iin,  es  de  ailvertir  ipie  el 
hilo  movil  no  es  e.xactamenta  paralelo  al  hilo  fijo.  Kstando  el  anteojo  dirijido  al  Xorte,  la 
estremidad  occidental  del  hilo  movil  queda  encima  del  hilo  iijo.  i  la  inclination  de  los  ihjs  hilas 
ascienda  a  0°T'." 

From  this  it  is  deducible  that  the  correction  to  the  observed  north  [lolar  distance,  on 
account  of  inclination  of  movable  wire,  is  negative  when  the  observation  is  made  before  meri- 
dian passage,  and  positive  afterward,  and  that  the  amount  of  the  correction  is  as  follows: 

lutt'ival  from  mcridiau.  Condition. 

.V.  " 

10  0.31 

'^0  0.61 

.•{0  O.U-i 

40  1  .-.'2 

50  i.oli 

00  1.84 

70  2.14 


10 


INVKSTKiATION    OF    THE    DISTANCK   OF   THE    SUN 


Kitlicr  tlii!  clock  tiiiif  (if  transit  or  the  vertical  wire  hoiii^  p:ivoii  for  all  extra  meridian 
oliservatioiis.  tlio  polar  ilistaiices  ohscrviul  with  the  movalile  wire  were  eorreeted  for  inclina- 
tion accorilin;;  to  the  aliove  talile.  It  was  noon  seen  tliat  the  efTect  of  this  correction  was  to 
prodnci;  Iar>-e  discordances  in  the  resnlts  for  i)olar  |)oint  deduced  from  tin;  several  stars,  and 
tills  ell'ecf  was  so  niiiforin  and  well  inarkeil  as  to  leavi^  little  doulit  that  the  correction  had  no 
existence  in  lact. 

it  was  then  foniid  that  some  correspondence  had  passed  lietween  the  Superintendent  of 
tlie  Naval  <  >l)servator\-  and  Mr.  Moesta  on  this  very  suliject,  in  18(U,  the  ellect  of  which  was 
to  tiirow  darkness  on  the  nature  ol' the  incdinatiou  correction  of  the  Santia^-o  Circle  during  this 
critical  |)eriiid. 

1  next  attempt!  d  to  determine  the  inclination  from  observations  of  the  same  star,  made  on 
dilVerenl  siiles  of  thi'  meriilian.  To  ellect  this,  a  tal)l(>  was  drawn  n\>,  showinj^  the  hour  angles 
of  .Mars  and  I'ach  of  tin'  ei;j;hl  stars,  for  each  of  the  Santia<;-o  observations.  It  was  found  that 
I'he  same  star  was  nearly  always  ohx'rved  with  ^reat  re^'ularitv  on  the  same  sidi-  of  the  meridian, 
it  was  not  |iossiiile.  therefore,  to  determine  the  imdination  of  wires. 

The  foll(;wiii^^  plan  was  adopted:  In  each  determination  of  the  polar  point,  the  inclination 
of  the  mean  of  the  wires  was  included  as  an  uid<nown  (plant ity  midti|ilied  by  a  numerical 
coeilicient.  etpial  to  the  mean  of  the  hour  annh's.  Tiie  correction  to  the  polar  distance  of  Mars 
was  then  e(pial  to  this  unknown  quantity,  multiplied  b\  tiie  dill'erence  of  hour  angle  between 
Mars  and  the  rest  of  the  stars.  The  stars  whose  hour  angles  were  i'arthest  from  that  of  Mars 
were  then  rejected  in  such  nundn-r  that  the  sum  of  the  coellicients  of  the  inclination  should  be 
(piife  small  for  eaidi  serii's,  mid,  as  nearly  as  practicable,  vanish  entirely  for  the  mean  of  all 
the  oliservations. 

§  5. 

The  Norlli  I'olar  Distances  of  Mars  thus  deduced  from  observations,  with  tiie  resulting 
iMpiations  of  condition,  are  given  in  Table  III. 

The  first  column  of  this  table  gives  the;  mean  solar  date, "the  day  changing  between  the 
meridians  of  Washingttui  and  Williamstown. 

'I'he  third  column  gives  the  seconds  of  North  Polar  distance  of  Mars,  derived  in  the  way 
set  forth  in  the  last  section. 

Following  these  are  the  multipliers  of  the  equations  of  condition  to  reduce  them  to  the 
same  probable  error.  These  niultiidiers  are  inversely  as  the  concluded  probable  errors  of  the 
positions  of  Mars.  They  are  on  a  scale  of  I  to  3  oidy,  as  it  did  not  seem  worth  while  to  attempt 
dividing  the  observations  into  ni(M-i>  than  three  classes  with  respect  to  excellence.  The  multi- 
pliers are  assigned  by  tiie  following  considerations: 

1.  The  nu'an  error  ol  an  observation  at  any  one  Observatory,  as  deduced  from  discordance 
of  results  for  pohir  jioints  derived  from  the  several  stars  observed  on  anyone  evening, 

*J.  The  number  of  stars  on  which  the  polar  point  depends.  The  omission  of  several  stars 
does  not.  however,  seriously  diminish  the  multiplier,  unless  the  same  stars  are  missed  night  after 
night,  so  that  tli(>  final  result  of  the  W(uk  with  any  one  instrument  will  depend  on  too  few  stars. 

.'{.  The  notes  of  the  observers  with  lespect  to  the  ((uality  of  the  images.  The  precision  of 
the  oliservations,  however,  appears  to  be  much  less  ailected  by  this  cause  than  n)ight  bo  sup- 
posed. The  greatest  extremes  of  ilescri|)tion  occur  in  the  Cape  observations.  Here  it  is  found 
that  the  mean  discordance  on  six  good  nights  is  ()".37;  while,  on  six  nights  noted  .is  very  bad, 
or  deplorably  bad,  it  is  0".35.  Here,  at  least,  the  elfects  of  the  cause  in  ijuestion  would  appear 
to  be  entirely  masked  by  those  of  other  causes. 

4.  The  number  of  observers.  There  being  always  a  possibility  of  personal  difTerences  in 
the  measures,  greater  weiglit  should  be  given  to  a  series  made  by  several  than  to  a  similar 
series  made  by  one  observer. 


4 


AND    THK    Kl.KMKNTS    WHICH    DKl'KND    IH'ON    IT.  1  1 

Tliu  first  c()nsi<l('ratioii  was  the  fiiinlaiiiotital  one.    Tlic  mean  orrurs  lor  the  dilVcront  oliser- 
vatious  were!  f'ontid  to  ho  as  follows: 

// 

Pulkowa 0.31 

Hclsiiif^fors ().7.'i 

J.eiden ().;j;i 

(Treonwicli Of).'! 

Albany 0.(i  1 

Washington ().')(» 

Williamstown 0.37 

Cape 0.;!(; 

Santiago 0a'>2 

The  adopted  multiplier  is  supposed  to  carry  the  mean  error  of  each  ecpiatioii  to  i.hout  ()."'.). 
The  next  eoluimi  gives  the  comi)Uted   parallax  in  polar  <listanee  for  the   ohservatioii,  the 
adopted  constant  of  Sun's  equatorial  horizontal  parallax  bein^ 

8".fiO. 
The  following  ai'e  the  adopted  co-ordinates  of  tlu;  dilferent  ohservatioiis: 


01)8erviitoiy. 


Willinmstowii 
Piilkdwa  . 
Helsiiigl'or.s    . 
Capo    . 
Leiden 
GiL't'tiwich 
Saiitiiipo    . 
Allmny 
Wusliington   . 


—  :!7  41.0 

tin    0.  a 

—  33  45.  4 
.'il  iV.  3 
r.l    17.4 

—  :w  10.  1 

4i  '2ri.  4 
38  4'i.  5 


a* 

o 

.J 


it.  !»'.n>i(i 

!».  Wr"M) 
!».  K'.ls'.tU 

it.  D'.IOlO 
'.». '.l'.MII-.i     ; 

;).  '.uc.i.'.i;   i 
!).  '.mr.n    ' 

'.I.  It'.CJlH     ' 


it.    m.     R. 


—  7 
0 


:!8    30 
0      (» 


-f  0     -21     28 
a    47    2:$ 


1  43  21 

2  1  11> 
0  43  .-.I 
0  ."i()  18 
7  It  3n 


3  « 

cc    O 

in 


rf. 

—  .3i.-i;i(> 

I        .0011(10 
+  .014UO 

1      .o;f2!»l 

1       .07177 

•o,-^i-r> 
I     ,  y.-'o.'.o 

.2Hitl(» 

'       .  2'.tH-,>7 


Next,  we  have  the  polar  distances  of  Mars  given  by  the  ejdiemeris.  In  the  adopter!  method 
of  discussion  it  is  essential  that  the  differences  between  tlie  ephemeris  and  the  actual  position 
of  the  planet  should  vary  regularly  during  each  period  of  twenty  days.  To  insure  this,  heli- 
ocentric ephemerides  of  the  Karth  and  Mars  were  computed  by  Mr.  Charles  Thirion,  aid  at 
the  Naval  Observatory,  for  every  other  day  during  the  parallax  observations,  using  Le  Verricn-'s 
tables.  In  the  ephemeris  of  tlie  Earth  the  planetary  [)erturbations  were  smoothed  off  by  dif- 
ferences, while  the  lunar  perturbation,  instead  of  being  taken  from  the  tables,  was  rigorously 
computed  from  the  co-ordinates  of  the  Moon.  In  the  Mars  ephemeris  the  perturbations  of  each 
separate  planet  were  mainly  developed  in  powers  of  the  time,  to  reduce  the  accidental  errors  in 
the  last  place  of  decimals,  produced  by  adding  so  many  terms. 

Com])aring  these  positions  with  those  of  Winneeke's  ephemeris,  the  variations  of  the  dif- 
ferences from  the  desired  law  were  found  to  be  altogether  insignificant,  seldom  amounting  to 
0''.02  in  longitude,  and  still  less  in  latitude.  I  still  feared  that,  as  Winnecke  used  but  seven 
decimals  in  computing  his  geocentric  plans,  the  imperfections  of  the  last  decimal  might  have 
affected  his  declinations.  Differencing  his  two-day  ephemeris,  the  accidental  errors  were  found 
not  to  exceed,  on  the  average,  0".02,  so  that  their  influence  would  be  altogether  insensible. 
His  ephemeris  was  therefore  adopted  as  a  basis.  From  the  right  ascension  ol)servatioiis  made 
at  Pulkowa,  it  appeared  that  the  tabular  heliocentric  longitude  of  the  plan<>t  was  too  great  by 
about  2".  40. 


I 


if 


IJ 


INVKSl  KiAl'KJN    OF    TIIK    IJISTANCI':    OK    TIIH    SUN' 


(|;IV: 


Sii|i|iii-iii--,    ilii'i-.^rni-c,    iImI    ilir    lii>li<ic(Mitric    loiiii-itiiilt'    ri'ipiiri'il    the    i-mi-tiiiil    fiiiTr''tiiiii 

'.■},    till-   <  \]\  r\    u|     tlii^   ll{Mi|l    llir   U'cdCflllric   IKil'tll    |H)l;ll-  ili^tillirc    W.K  C  ):il  |ilU  I'l]    lor  OVlTV    tlMl 

;.   with  iIh^  liilKnvinu-  roiill  : 


uo  1 
n\rr 


JS(i-.'.   Au>,'iist            IS,  +:.'.;!•>; 

:>\  :i.&^ ; 

ScittcmlMT       7.  2.U-2 ; 

]7,  .•{.!;'.: 

27,  :i2l; 

Oftohcr           7,  ;;  k;  : 

17,  :.'.(»;! : 

:i7,  2.(')0; 

■Novcinbor        (i,  +:i.2.s. 

'I'lioo  ((inectidiis  liciiii:-  iiitiTiniliitoil  to  cvcM-y  duy,  ainl  applidl  to  WiiiiKvke'.s  K|ili(>iii('iis, 

lavc    tlic    I'Mlldwiiii;-   ('|ili(Mni'ris  oi'    the    llicorctical  iiortli    jmlar  ilistaiirrs  dI'   Mar.s  at  transit 
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4.-) 

54.  S4 

From  flu-  abovi?  I'plu'iiuM'is  tlu^  positions  in  tlu>  sixth  colninii  were  coiii[mtefl  by  interpo- 
lation, using  th{>  aihipti'd  h)nj;itU(1('s  of  the  Oltservatorie.s  already  given. 


V 


AND   T1[E    KLKMENTS    WHICH    Dl  I'EM)    IJi'ON    11'. 


13 


I\  t'ormitif^  tlio  equations  of  (MiiKlition,  tlw  oliscrviitions  ,ir(^  dividtMl  into  livi'  sciics.  Tlio 
first  two  scrios  coniprisc  tlio  ohsi'ivations  iiiiidc  uitli  tlio  first  ^r()ii|i  of  Wiinu'ilju's  coiii|iiirisoii 
stills,  iuid  tlio  next  three  tliose  iiiade  witli  tlie  tiirec  t'oilowiii^  groups. 

Ill  roriiiiii^  tlie  e(|Uiitioiis  of  coiidilioii,  tiie  errors  of  tlic  iiortli  polar  (listaiice  of  tlie  oplioin- 
eris  proved  to  lie  so  inimite  that  the  simple  error  of  ^'■(>oeeiif rii'  declination  was  introduced  into 
tlio  iMjiiations  instead  of  tiio  tM'ror  of  ihe  liiu'ar  co-ordinato  ;.■,  which  it  was  intended  to  use. 
The  three  uiiknowii  ciuanlities  in  the  ecpiations  aie  a>  follows: 

M,  the  error  of  north  polar  distance  at  the  middle  d  itu  of  i-acli  series. 

/9,  the  change  of  a  in  ton  days,  siqiposcd  constant  tliroup;hont  oacli  series. 

-',  the  error  of  the  Sun's  mean  equatorial  hori/.ontal  parallax  dividend  Iiy  O.S'.t. 

The  (general  form  of  the  equations  of  condition  is 


0=p|«+/,,H«:!^-;p:-+J.N.IM,.} 


where 

P=:  measure  of  precision,  (column  4  ) 

/=:tiino  in  days  from  the  middle  of  each  s 'lies. 

;;'  =  planet's  apparent  pjeocentric  zenith  distance  south. 

J.zr  planet's  distance  from  the  earth. 

J.N.P.D.  =  the  coinpute<l,  minus  the  observed,  geocentric  north  polar  distanc.n. 


S.. 


> 


14 


INVK8TIGATION    OF    THK    1)1.STAN(;H    OF    TME    SUN 


Comparison  of  }sorlli  Pnhir  iliilitinex  of  Mara  ilvrirn]  frmn  ohsirrution  with    those  giriii  hij  the  Hphemeris, 

iind  J'Jtjitations  of  condition  iiirm  hij  t/ir  lonijiiirison, 

FIRST  SKK'IFS. 


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+0.8 

Saiitia;r<' 

]ti.!> 

•> 

+  11.!) 

•27.  (lit 

.. 

+0.  H          — -J.  1 

•)^  0 

Albany 

4o.:i7 

I 

—   l'J.77 

•i".  I-' 

1 

+0.4         +1.:! 

+(T  i\ 

Wasliinfjtdii 

40.  .VJ 

2 

—   Il.7'i 

•^n.  7:! 

■> 

+0.  s        +■,'.  3 

—0. 1 

(i 

AVillianisti>«  11 

:!7.:i7 

1 

+  i:(.  li> 

.V,'.  14 

I 

+o.r.       -1.!! 

+1.6 

\\'iisliinijtciti 

4:..  '-'S 

0 

—  Il.rti 

:u.(ii 

0 

+  1.0        +','.4 

+1.1 

t 

Saiitiaffo 

:tit.  4 

») 

+  1','.  1 

.-.i.:« 

>_> 

+  I.'J        -','.4 

—0.3 

Alliiuiy 

w.m 

I 

—  I'J.iM 

r.'i.(ii» 

0=ln, 

+(i.(U,    +i.:tT' 

+1.1 

AND    TlIK    KLKMKNTS    WIIICII    DKI'KNO    UPON    IT. 


ir. 


IIKS 

r  si;kii:s-c. 

iitiiiiii'il. 

1*         ; 

1 
t 

11  r 

Diitr. 

OliMi'ivatory. 

1!    i 

_. 

5 

1 

=  J,  a 

'  a^ 

Ki|iiatiii|is  III  riinilllinii  ^Ivrii 
iili.scrvalii.iis. 

l.y  till' 

n-z  t 

'■/. 

~ 

"  -  a 

1  =  3 

V 

= 

c  il 

J'. 

- 

w 

Ju 

|H(lV». 

Sf|>t.    t^ 

Williiiiiixtowii 

ii.i;i 

I 

+  l:i.:ti 

•jr..  iw 

II.    Ill,      +11.7  (, 

—  I.ISt- 

+  l."7 

('ii|ii'      .... 

111.  <>ii 

*» 

-f  I-,'.-.'- 

,'.;i.  :i.'. 

2         +1.  1 

—2. .'. 

+11.  - 

Siiiiliairo 

11. 1 

+  1  •-'.•.' 

•,•:!.  It- 

1         +11.7 

-- 1. 2 

+  0.  1 

Alliaiiy 

:i(  ;.•.'•.' 

—  111.  II-.' 

•,M.  •.'•.' 

1         +11.7 

+  l".'l 

+  l.i» 

\Vilsliil|i,'liiII       . 

:«■..  17 

—   II. '."7 

•J.-..  1 1 

+  1.4 

+•-'•  1 

+  1.11 

1) 

Allpiuiy 

'jii.  11". 

—  l:i.  II 

'.1.  17 

1          +(•.■' 

+  1.:! 

+2. .-. 

III 

\\  illiainsdiwii 

\i  .  :\o 

+  i:!.  1- 

.'.4.:!l 

2         +1.7 

•2.7 

+  1.1 

I'lllUliVMl 

■III. :)',» 

—  l7.-.';i 

:w.  1-.' 

;i        +2. 7 

+.-..  1 

+11.1 

Li'iilt'ii  .... 

r.r..7(i 

—  1. ■..!.:! 

III.-.' 

2         +1.- 

+:i.  1 

+  1..". 

•  ilriiiw  irli 

r»7,  i'lfi 

-  ir..  Ill 

4'.'.  ;i.-. 

1          +11.11 

+  1..-. 

+11.  2 

Allmiiy 

aii.iJi 

—  iii.'.'ii       1 

7.. Ml 

1          +'1.11 

+  1.:! 

+  0.1 

II 

Williiiiii.'itdwii 

ii.'.ii 

+    111.  .Ml          1 

.".7.  :!n 

+  1.11 

.)    *■ 

— 11.  - 

I.i'idi'ii  .... 

;i.  17 

-   I.-..7-J        i 

4-.  7-.' 

2         +2.11 

-\--\.  1 

+2. .-. 

(tici-invirli 

"..  Ill 

—  I.-..  Ml       ; 

.Ml.  1(1 

1          +I.II 

+  i.r, 

+ii.r. 

1',' 

I'lilkdWii 

ir..  1.'. 

-   17.111 

r.s.  ;in 

+2.  2 

+:i. .-. 

—  0.  •'> 

lli'Miifrtiirs       .      . 

IT.'.l-i 

17.. '.7 

II.  .Ml 

1          +1.  1 

+  1.^ 

+11.2 

(.'iipi!      .... 

.'.II. -1 

+  1  •.•.:.■.'      , 

:!.  17 

:!       +;!.:i 

It     ^ 

— II. .'. 

Lciilcn  .... 

•ji.  r.i 

ii       —  i:..-i       1          .-.-4 
SKL'OM)  si;i;ii:.s. 

1)    ;;„,     +:i.  :u, 

+  'i:7r' 

+  1-1 

+  1.0 

Si'pt.  i:t 

WilliaiM.^liiw  11 

V'."..  1»7 

•> 

+    IH.Il- 

111.  14 

0^2.1.     — 1.  1  <■ 

■.'.7t 

I'lilkiiwii 

17. 'JC. 

\\ 

—   17.  .V.I 

•,'1>.  17 

:t          1..". 

+.-..  li 

— 11.  (1 

Hi'lsiiifjliii's 

4f.  .-"> 

•» 

—   17.117 

:ii.-j 

2         —I.ll 

+;i. .-. 

+  l.:i 

('iijif 

','l.ii'> 

:! 

+   |-i..".7 

:i4.iii 

:t           1..-. 

+:i.  2 

Lridcll  .... 

.Ml.  ^,'. 

:! 

—   1.'.. '.Ml 

111.7.". 

:i       —1..". 

+  i'.  -^ 

— 0.  11 

Siiiitiiijro 

I.ll 

1 

+   l-.'.4 

Iil.ii:! 

1        —11..". 

-1.2 

II.  1 

Wiisllill^rtdli 

V!-.  >7 

tj 

—  I'.'.  :m 

111.  7li 

2          -1.1' 

+•-'. .-. 

+  0..-. 

II 

WilliMIMSiO-.Vll 

.-,.  :w 

:! 

+   i:;.7l 

l-.',ll 

:;       —1.;; 

—  1.  1 

— 0.  ll 

I'ulUiiwii 

•v'!l. '.Hi 

:i 

-    17. IIS 

ll.'.M 

:!       —1.2 

+:..  ;i 

-    1.0 

Liiilcii  .... 

:!'.l.  7ri 

•> 

—  l.-..'.i'.l 

•24.  ii-.i 

2             II.- 

+:i.  2 

+0,.-, 

Siiiitiil^'ii 

•17.0 

T 

+  i-'.r. 

;".'.».  .Ml 

1       — II.  1 

—  1.2 

+11.  II 

1") 

Williiiiiisliiwu 

iVi.-.>l) 

•> 

-f  i:i.7;» 

-.11(1 

2         —11.7 

..    w 

-II.  1 

I'lilkiiwii 

•Si.  lili 

•} 

--   17.77 

."..-.".I 

2         —II.  11 

+  :'!!.-. 

— 11.  ll 

Liiiliii  .... 

:t:!.  !»7 

~i 

—   HI.  iw 

1-.  14 

1!          —Il.lt 

+  l--^ 

+  0.  ■' 

Wasliiiicton     . 

1'.'.  lit 

•) 

-    I-J.  H 

.".'.I.OI 

2       — II.  r. 

+2. .-. 

—  I.:i 

III 

Williaiiistiiwii 

".."..  7;i 

;i 

+  i:!.-;! 

11.  4.". 

:!       -11.7 

-1.  1 

—II.  :i 

I'lilUiiwa     . 

•,'7.llf< 

4 

—  17. -II 

11.  Hw' 

:;       —11.11 

+.V  1 

— II.  t; 

Li'iili'ii  .... 

:w.  -It; 

:i 

—  1(1.  Ill 

•i-i.  .".II 

:t       — (1.  ti 

+  I.H 

+11.11 

(ill't'llW  iili 

tii.i;:! 

1 

—    III.  III! 

•.'l.lllt 

1         —11.2 

+  1.11 

+11.4 

Sanliiip"     . 

.'.11. 1) 

1 

+   I'.MI 

•.'.  :i.-. 

1         —11.2 

—  l.:i 

—11.2 

17 

Williaiiistiiwn 

li.  Ilti 

a 

+   l:i.>7 

III.  ss 

:'.       —11.4 

4.  1 

—11.2 

I'lilkiiwii     . 

411. -^f) 

3 

—   17.  H4 

2-.'.  4- 

:(       — (1.  :i 

+.-..  I 

+  0.  1 

Ilclsinp;l'(irs 

44.  .^.8 

1 

-   17.  IW 

2.-..  44 

1           II.  1 

+  1.- 

—  1.2 

Li'iili'ii  .... 

W.  '.'a 

1 

—  m.-ji 

:iii.7:t 

1        -11.  1 

+1.11 

+  0.- 

(ill'fliwicll 

r..-..  r.-.> 

1 

—   111.  07 

nil.  '.'It 

1        —II.  1 

+  1.11 

—11.  2 

1  Sanfm^'ii     . 

r».  f) 

1 

+   I -.Ml 

I-.  IJ 

1        —II.  1 

—  1.:! 

+0.;! 

18 

I'lilkiiwii 

•,'.  44 

li 

—   1-*.  ii'J 

4."..  Ill 

:s          11.0 

+.-..  1 

+  !•- 

i   llflsiii},'('i)is 

.'■..  l»5 

1 

—    IS.  111! 

4s.  Ill 

1           11.11 

+  I.S 

+0.2 

j  t'api!      .... 

:ti>.(i:! 

:j 

+   I-.'.  711 

51.-2 

;!          0.  II 

— :i.  s 

+11.  1 

!   I.i'iili'n  .... 

If..  4H 

:; 

—   111.  lil 

.V.I.  si» 

:t          11.0 

+ 1.  It 

—  0.  -^ 

\Vusliiiii;tiiii      . 

(1.  :tii 

•J 

—   1-J.(l'.l 

47. 1 H 

2             11.0 

+2. .". 

—1. 1 

1!» 

Williaiii.stDWii 

r.:t.  ti:{ 

:{ 

+  i:i.ic. 

7.  iri 

:!       +0.2 

—  1.2 

+1.11 

•   rulkdwa 

:m.  i»7 

:i 

-       IS.  (!'.» 

1."..  112 

:!       +11.:! 

+.-..  4 

—2. 11 

,  Ciii.i'      .... 

III.  It) 

:s 

+   |-.'.7s 

22.1111 

:!       +11.  :i 

— :i.  s 

+11.2 

j  Li'uli'ii  .... 

4^.7.-. 

1 

—    Ifl.liS 

:tl.:!ii 

1             +0.  1 

+  1.11 

—  1.0 

]  Santiagi) 

.-..  :i 

1 

+   l-.Ml 

ir..,".i 

1            +0.  1 

— l.ii 

—  1.  1 

iill 

1  Li'iili'ii  .... 

•M.  (1(( 

;i 

-   111.11 

lii.4li 

:i        +o.(; 

+ 1. 11 

+11.7 

8aiitiai;ii 

411.  1 

'i 

+   I--'.  7 

.'■.7.  IIS 

v!        +11.4 

—2.  ."> 

— :t.  I 

yi 

Williamstown 

i:!.l>4 

u 

+   14.1111 

27.  47 

2        +"■•'' 

— 2.  S 

—ii.lt 

I'lilkiiwa     . 

.>-.  17 

:» 

—  l-.-.'J 

nil.  Ill 

:(       +11. '.1 

+.".. .". 

—11.  1 

Albany 

r.".  r.() 

1 

—  I:!.'.i7 

411.  2.'. 

1         +:i.:i 

+  1.4 

+  1.7 

'   Washiuptou      . 

•,'.  4-^ 

1 

—  I-J.s.-. 

4s. :!.", 

1        +11.  :i 

+  l.:i 

—  1.2 

'ii 

'  I'lilkowa     . 

r.ii.4:i 

=' 

—  IS.  27 

:{|.:w 

O—Wui      ■\-\.-i.ii 

+:..  .-.T 

— .'.  :i 

16 


INVKSTKIATION    OF    TIIK    DISTANCE    OF    THE    Hl'N 


HKe'OND  .SKIMKS— ('..ntiniiiMl. 


7i 

, 

i 

^     Hi 

Uiiti', 

( •l).>ii'i\  iitdiy. 

■~  2. 

1 

i 

=  11 

1         "y  J-  i 

Hi|iiatii.iiM  III  ciiiiilitiiiii  (i^ivcu 
iilistu'valioiiM 

l.y  tlic 

=  E  2 

1    z    S 

;2 

s 

c 
0 

!     1^"^ 

l^ty. 

1 

i 

// 

Srpl.  •,'•.• 

llilsiiiirriHs 

:.i.  i-* 

1 

-  i«.  :t(i 

:ti.^'s 

0—1  </j 

+0.H:      +I.Ht' 

+  I.H 

Ciipr 

•.'.'..  f(i 

:< 

+    la.KI 

:i'.t.  10 

;{ 

+  1.','          — '.f.  H 

+  I.'J 

l.ridrli 

1 

1 

-    1(1.  .V. 

■I'-.'.M 

1 

+0.1          +1.7 

—o.>* 

(Jiriiiwicli 

(1.  it:. 

1 

—  It;.  :i;i 

r.i.  1:1 

1 

+0.   1            +I.<i 

+0.(! 

Siiiilia^'o 

m:>.  I 

1 

+   P.'.  7 

j        :t7.:io 

1 

+0..I       -i.:t 

—0. .''. 

Alliiiiiv 

M.  Iti 

1 

—  11.02 

it'.t.  :i-.' 

1 

+0.1       +1..1 

+  \.'i 

W,i.sliili;rtiiri 

r.i.  10 

*> 

—  IV. '.to 

11.17 

t> 

+  0.H        +v'.ti 

+0.4 

'.':i 

W'llluiiiisldwii 

^t^.i^i't 

;i 

+   II.O'.! 

:      I.'.  17 

:t 

+  1.4        -l.-J 

+0.!l 

I'lilkonii 

17.  •I',> 

0 

—  |H.:fi 

'.*^.  (II) 

*» 

+  1.0       +:i.7 

o_  •) 

Clip!' 

'.':i.  :w 

:i 

+    I'.'.HI 

1        ;t.'..  -ll 

'i 

+  1..-.      — ;i.  H 

— 0.!l 

Lriilcn  . 

II.  <)i 

1 

—    Itl.til 

1        -i.-..  Hi 

1 

+0..-.        +1.7 

+  0.  H 

( ini'iiw  ifli 

1.  II 

1 

—   It!.  IJ 

•1-.  IC. 

1 

+0.,-,         +1.1; 

+  ».-i 

SllMtill^'"!! 

'.'■-'.  '"^ 

1 

+   I-.'.  7 

:!.'..  1 " 

1 

+0..-,       — i.:t 

—0.  :i 

Allmiiv 

r.ii.  t;r> 

1 

—  N.07 

1        :i7.  •,'.-. 

1 

+0..-.       +1.1 

+0.7 

\\*MNliin(;tini 

.■.i.(ir> 

•) 

—  |-.i.!t« 

:i!t.  11 

0 

+  1.0       +-.'.r. 

+  i.r. 

','1 

Williiiiii^liiwii 

r.7.  r.ii 

•>    1 

4-  l-J.o-i 

11.77 

0 

+  1.1       —-i.rt 

+0.'. 

llil-iiiirliiis 

.-.1.  iv 

1 

—  |M.4(J 

:!••'.  1.'. 

T 

+  11.  f.           +I.H 

i).:, 

Ciipi' 

•.•:!.  7:1 

:t 

+   l-.'.sl 

;!i;.  ^> 

;t 

+  I.-1         -X'* 

+0.  H 

l.rjili'll   .       .       .       . 

•J.  i;t 

>. 

—  1(1.  tltl 

111.  ■,'(! 

.. 

+  I.V'      +;!.;! 

+  1.0 

Siiiili;i;;o 

M\.  :t 

>. 

+   |-.'.7 

:i7.ol 

0 

+  1.-,'      -•.'.:. 

+0.1 

All.iiiiv        .      . 

W.  7 1 

I    1 

—  II.  li 

:!'.!.  1-.' 

1 

+0.(i         +1..1 

+0.:, 

\VM'iiiiii(;l(iii 

r>:i.(;i 

'■i    1 

—  lii.  Hit 

4i.:i5 

U=->nj 

+  1.2,1,       +-<i.(iT' 

+i.r, 

TllIKU  SKK'Ii;.<. 


S..pt. 

.;.'      Williiinistdwii 

1          l.or. 

'      0 

+   M.0',> 

'          14.9:1 

0     -•,'«:, 

-1.  H:, 

—  >.><:r' 

—0.  :i 

lli'l>ill;;rcirs 

!       .".1.  i- 

\ 

—   I-..-.0 

:ii:.  lio 

1 

—0..'. 

+  1.^ 

+0.11 

Cape       .       .       .       . 

:       ','7.  in; 

0 

+    l-J.  K! 

4l.o-.> 

0 

—  1.0 

—2.  ti 

+0.;-. 

(in'i'liwicli 

'.Mi,-. 

•  I 

—   Iti.  .-.1 

i         :.:!.  ll-.' 

0 

—  1.0 

+:<.  :i 

+  1.0 

."-aiiliairo 

■J".  VJ 

** 

+   |-<.'.7 

I          41..-.^ 

•  > 

—  1.0 

--.'.  r. 

+•2. 0 

Alliatiy         .       .       . 

i            Eti."  I7 

:    1 

—  14.  Ill 

4::.  91 

T 

-II..-. 

+  1.4 

+-2.0 

Waslniifrton 

1            .^•^.  111 

1  t> 

—  i:i.ii;i 

1        4(i.-j;! 

»> 

— 0.  .-> 

+-2.tJ 

+■2.  -2 

■H'i      W'illiaiiisldwii 

7.  !•.' 

1  '*  ■ 

+  11.01 

•-'0.  (i.-^ 

~', 

-l.:t 

— 1.-2 

—1.1 

'   I'lilUdWu 

i           .-.-.-Jit 

!    :t 

—  1-.  41 

i         :i9.  :ti 

:i 

!.•,' 

+.^.  -. 

—1.4 

l.cicliU  .       .       .       . 

1:!.  17 

;j 

—   Iti.  7-J 

.-.7.  mi 

:• 

—l.-J 

+.-..  0 

+0.9 

.'^arilia^o 

:!ii.  ,-< 

•  ) 

+   l-.'.7 

4'-.  7-J 

•> 

— II.  s 

V.   .') 

-i.ii 

Alliaiiy        .      .      . 

:i.  1.-. 

I 

-    11.  lit 

,'.0.  f^:! 

ii 

—II.  4 

+  1.4 

+  i.ti 

Wasliiiif.'-liii] 

ti.  11 

•) 

—  i;(.  (Hi 

,-.:!.  1 1 

.» 

— 0,  8 

+-2.li 

— 0.  r. 

J7      ^\■illi,•llrlslll^vIl 

i:!..^:! 

•> 

+  14.00 

y.-.  09 

•J 

—0.7 

— -2.  f' 

+1. 1 

Piilkdua      .       .      . 

.-..  1,-. 

•> 

—  l-.4(i 

47.04 

.) 

—0.(1 

+:i.7 

+0.1 

1  Ii'Uiii^,''r(ir,s 

|0. -."J 

0 

—   !>..-.t! 

r.o.  74 

0 

0.  (i 

+:i.7 

—1.8 

l.iiilcii  .      .      .      . 

•Ji.'-'-i 

;; 

-   Hi.  7.-. 

4.  >,-. 

li 

—0.9 

+r>.o 

+  1.0 

.""Miiiiat,''! 

!         i;;. :! 

1 

+   I-.'.  7 

.-.(i.  or. 

I 

-0. :( 

—1.:! 

+0.7 

.Mliaiiy 

;           ll.ii7 

1 

—   14. -,'1 

.-)>.  78 

1 

— 0.  :i 

+  1.4 

+1.3 

is         Wllli.-llMSldWIl 

!           -JLiilt 

0 

+  i:!.ii-' 

:iii.'-'o 

*> 

—0..-. 

—-2.  8 

+1.7 

I'lilkdua      . 

1:!.  .-.1 

•J 

—   M.4S 

,-.,-..  k; 

•> 

—0.4 

+;!.7 

+0.2 

Ijclsiiifrl'i'i-s 

ii.:il 

•1 

—    1 H.  .->r< 

.-.8,  Si 

•j 

—II.. I 

+:{.7 

(+li.-2) 

i   .'<aillia;;-(i      . 

1           .M.ii 

0 

+    1  ■,'.(> 

4.71 

»> 

—0.4 

—-2.  r. 

+  1.0 

Wasliiinrlon 

•-'■-'.  HI 

11 

—    1:!.  II 

9. 1 1 

I 

—II. -J 

+  i.:{ 

—0.7 

',",t      W'illiaiii.sliiwii 

1        'Jit.  r.:! 

»i 

+  i:i.!t(i 

44.04 

\> 

— 0. '2 

—2.r^ 

+  1.1 

I'lilUiiwa 

!             V'l.K". 

:! 

—  If'.  411 

■.'.  7-> 

:1 

—0.  :i 

+-,.ry 

—  1.9 

llflsiii(;l'oM 

•,>:!.  :io 

•.' 

—    lH..-.il 

ti.  40 

•> 

— 0.  ^2 

+:i.7 

+:t.4 

I.iiilcii  .       .       .      . 

'        :i7.o:! 

•> 

—  Iti.71t 

•-'0.  4.-. 

2 

—0.  -2 

+:i.  4 

--(t.4 

\Va!-lMni;'toii 

[        :!o.  \■^ 

\ 

—  i:{.  14 

Hi.  :u 

1 

— (t.  1 

+  1.:! 

—0.7 

; 

!0      Williainsluwii 

:!7.  1.-. 

a 

+  1:1.9:1 

-.0.1  i7 

2 

0.0 

—2.>i 

—0.  8 

;   I'lilkiiwa     . 

•,'7.77 

•■i 

-   18.49 

8.77 

•2 

0.0 

+:!.7 

—  1.0 

Santiai,'!) 

.-..  1 

1 

+   i'2A\ 

17.4;.' 

T 

0.0 

— i.:i 

— o.:i 

Got. 

1      WiHiaiiislown 

i           11.17 

•,'    1 

+  i:i.lio 

-).-..  17 

0 

+0.-2 

—-2.8 

+1).  2 

I'lilkowa 

i        :to.  lio 

:{ 

—  18.49 

1-2.41 

ii 

+0. :! 

+5.  5 

+0. 9 

l.riiltMl  .       .       .       . 

!           47.41 

2 

—  H!.80 

•29.  78 

•2 

+0.-2 

-  -3.  4 

-17 

!>      WilliaiMslowii 

4:;.  44 

3 

+   l:!.87 

Til).  (i7 

Ti 

+0.  (i 

—4.1 

—  .9 

^  Cajic      .      .      .      . 

s.  19 

.i 

+   IV-'.tiH 

•20.  til 

:i 

+0.() 

—3.8 

•  -0.  ri 

:  Saiitiapii     . 

ii.lt 

1 

+  1  •.».;-. 

19.49 

1 

+0.  2 

—1.-2 

+(t.i 

!  Wiisliinfjtoii 

:tf..  r.7 

1 

-i:U5 

•-':t.  70 

0=:2a:x 

+0.  4A 

+2.  (i:;-' 

+0.  t! 

^ 


AND   THi;    ELKMKNTS    WIIICII    FH'.I'KND    I'I'OV    IT. 


17 


v^ 


nilKD  .-JKUIKS-C. 

(Iltiniled 

, 

>-3 

"1-2   . 

3  5  ?- 

Dnto. 

01)Ht'rvatory. 

31. 

d 

1 

^    a 

r.ipiiiiioi 

M  oC  cnuditidii  givei 
nliNel  \  alioiiH. 

h.V  till' 

"o-a  ? 

0 

'1  f  ■- 

B  C  2 

'.% 

V 

-<   r  s 

V 

i 

r 

• 

1H<W. 

'* 

Oct.     :i     Williiiiiistown 

III.  1 1 

o 

+ 

i:i.83 

.'.l.'.'-i 

0-  .2« , 

+  0..'..*:, 

•,>.  H~i 

+0.7 

1  Cftpi-      .... 

l.lll 

o 

+ 

l.'.fll 

Hi.  01 

•J 

-fii.  Oi 

— 2.  .5 

— 0.1 

4  1  WilliiiiiiHtnwn 

:w.  '.>v! 

•  > 

-f- 

13.78 

47.  I-.' 

o 

-j-ll.  H 

—2.8 

+0.8 

I'lilkowii     . 

M.  (i7 

\\ 

H.44 

0.  HI 

3 

+  1.2 

+5.  5 

—0.  1 

Ili'lsinirl'iii's      .     . 

lit.  HH 

1 

— 

II..M 

3.  ,'.0 

1 

+0.4 

+  1.5 

—  1.8 

r. 

WillJlllMStOWll 

•->l.  II 

1! 

+ 

13.73 

31.3.-. 

3 

+  1.4 

I.  1 

1.5 

Ciipi'      .... 

41.  Ill 

:t 

+ 

l','.r)3 

Wi.  07 

3 

+  1.5 

—3.8 

—2. 11 

Leiden  .... 

1^-.  C.-J 

1 

Hi.  73 

1 .  •»• 

1 

+0.5 

+  1.7 

—0,0 

Smiliiipd      . 

:t.i.(i 

1 

+ 

\-<.\ 

47.  I-J 

1 

+0.5 

1.2 

+0.4 

fi 

rulkiiwii     . 

!•.>.  i:i 

:t 

— 

18.37 

yi.oii 

3 

+  1.8 

+5.  5 

—0.2 

llelsilipfors 

•1."..  oil 

1 

— 

I-.47 

a7.ai 

1 

-t-0.  r. 

+  !.'< 

+0.  0 

Ciipe      .... 

I7.f.l! 

:t 

+ 

I-J.48 

31.07 

3 

+  1.^ 

—3.7 

+2.  8 

Leiilon  .... 

ri.'i.  77 

;! 

— 

Hi.  70 

311.  12 

3 

+  1.'* 

+5.  0 

+  1.0 

tSaiitiH|r<)     . 

IV'.II 

1 

+ 

!•,'.  3 

24.  03 

1 

+ii.ii 

-  1.2 

0.3 

WiiHliinfrton 

11.7(1 

1 

— 

13.  10 

27.77 

0-_l(i, 

+  0  lif, 

+  I.3T' 

—0.8 

FOLK' 

I'll  SKKIKS. 

Oct.     7 

hoicleii  .... 

'.T).  :t7 

3 

_ 

Il).(!(> 

10.03 

Ov-^304 

-i.8,y, 

+5.  On-' 

+0."8 

Siiiitinffo 

41.  1 

1 

+ 

IV'.3 

-.2. 117 

1 

—0.0 

—  1.2 

—0.4 

Allmiiy 

7.  I\> 

1 

14.  17 

r.4.71 

1 

—0.0 

+  1.4 

+  1.8 

Wii.sliiii<rtoii     . 

11.  H(l 

1 

— 

13.08 

5(i.  ,".8 

1 

-0.0 

+  1.3 

—0.  1 

8 

WiU'miiistown 

r.it.  •;.") 

3 

+ 

I3.r.ti 

13.41 

3 

-1.0 

—4.  1 

+0.0 

Leiden  .... 

4"'. ;«; 

3 

I'i.tia 

32.  34 

3 

—  1.5 

+5.  0 

+  1.8 

Siintiiifji)     . 

II.  !• 

1 

+ 

la.a 

13.43 

1 

—0.5 

—  1.2 

+0.  3 

Alliiuiy 

i.»H.  :i7 

1 

— 

14.13 

1.-..  1 1 

1 

—0.5 

+  1.4 

+0.9 

Wii.sliiiiptoii     . 

i>7. 7(i 

1 

— 

13.0.'-. 

10.111 

1 

—0.  5 

+  1.3 

+2.  a 

9 

Williiinistown 

is.:i7 

3 

+ 

13.  4'J 

31.28 

3 

—  1.3 

—4.0 

—  1.7 

Ilelsiiifjldift 

r>:!.  \n 

1 

18.31 

34.  83 

1 

—0.  4 

+  1.8 

—0.8 

Leiden  .... 

•.'.  Ill 

3 

— 

lti..'iti 

45.00 

3 

—  1.2 

+5.0 

+0.2 

WiLsliinpton 

40. :{.") 

a 

— 

l3.oa 

27.  nil 

•1 

—0.8 

+2.  r, 

+  1.3 

10 

WillianiHlowii 

'l\.  'iS 

a 

+ 

13.4a 

38.  02 

*) 

—0.7 

—2.7 

+  1.8 

Ciipu      .... 

•J'.l. !».". 

3 

+ 

l-J.'.'-J 

42.08 

3 

-0.  It 

—3.7 

—0.3 

Leiden  .... 

4.  87 

3 

It).  .'lO 

4i».OI 

3 

—0.9 

+.5.  0 

+  1.11 

Siiniiiipo 

1 :!..'. 

a 

+ 

1-J.O 

20.00 

2 

—0.0 

-2.  4 

+  1.0 

11 

Williiinistown 

1i:i.  If) 

a 

+ 

13.3.-. 

3.-..  7  I 

•) 

—0.5 

-2.  7 

+0.  5 

I'ulkowa     . 

47. :«» 

3 

18.07 

21t.  92 

3 

—0.0 

+5.4 

+  1.8 

llel.singt'ors 

4!).  7:5 

a 

— 

18.18 

3-J.  42 

o 

—0.4 

+3.0 

+  1.7 

la 

Willianistown 

f<.;ii 

a 

+ 

I3.a7 

21.118 

2 

—0.  3 

—2.  7 

+0.8 

I'ulkowa 

:to.  iiCi 

3 

n.ti'j 

12.  5i; 

3 

—0.3 

+5.  4 

0.3 

Cll))!!        .... 

r>. !)!» 

3 

+ 

ia.o8 

17.71 

3 

—0.3 

—3.  0 

-1.  1 

Santiiigo 

44.  4 

1 

+ 

II.  it 

5li.  00 

1 

-0.  1 

—  1.2 

—0.3 

13 

Willianistown 

4-2.7I 

a 

+ 

13.  1'.) 

!'.0.7I 

•.) 

0.0 

—2.  0 

+  1.0 

Ilelsiugfors 

4.  4r, 

1 

18.01 

4.-..  58 

\ 

0.0 

+  1.8 

-0.11 

Capo      .... 

:tri.  !»i( 

3 

+ 

la.oo 

48.  I!» 

3 

0.0 

—3.  0 

+0. 1» 

14 

Leiden  .... 

aii.  'jis 

a 

Ki.ai 

11.31 

>.> 

+0.2 

+3. -J 

+1.1 

Albany 

n-j.  -a 

1 

— 

13.80 

31>.5I 

T 

+0.  1 

+  1.4 

+1.1 

ir. 

I'lilkowa     . 

24.71 

3 

— 

17.71 

7.  33 

3 

+0.0 

+5.  3 

+  1.0 

Capo      .... 

f)'.*.  -it; 

a 

+ 

11.8". 

11.23 

2 

+0.4 

-2.  4 

+0.2 

Greenwich 

:i:!.  f 8 

a 

l.'>.  9.-. 

17.29 

»> 

+0.  4 

+3.2 

—  1.3 

Santiago     .     . 

!i7.  r> 

a 

+ 

11.7 

40.  11 

2 

+0.4 

—a.  3 

+  1.8 

16 

Pnlkowa     .     . 

10.  r.r. 

3 

17.60 

59.  22 

3 

+o.<» 

+5.  3 

+0.8 

Leiden  .... 

1W.5I 

a 

- 

10.  03 

0.  72 

2 

+0.0 

+3.2 

+0.  5 

17 

\Vasliinp;tou     . 

lo.lhJ 

1 



ia.o3 

3.  3'J 

1 

+0.4 

+  1.3 

+0.  0 

18 

Wiliiamstown 

'i.'ij)-i 

a 

+ 

I-J.74 

35.  35 

2 

+  1.0 

—2.  5 

+  1.2 

Washington     . 

\\->.  'i'i 

a 

la.  45 

22.  18 

2 

+  1.0 

+2.  5 

—  1.2 

19 

Cape      .... 

iVJ.Iil 

a 

+ 

11.55 

10.44 

2 

--I.2 

-2.  3 

—1.4 

Santiago     .     .      . 

13.0 

a 

+ 

11.3 

24. 83 

n=2n< 

+  L2A 

—a.  3jr' 

+  1.1 

18 


INVKSIKIATION    OK    TlIK    DISTANCK    OF    IIIK    HI'N 


nirii  -iiMi.s. 


■Si 

~it  . 

f^ 

K 

-    3    2 

I>llt 

1', 

Oli-ll\lll(il\V. 

.3 

1 

hi 

a  ~ 

l'',c|iiatiiiiiN  III'  I'liiiditliin  irivi'ii 

iilisi'i  valiiiiii. 

liy  till' 

s  n  i 

_/. 

?    i  s 

V 

B* 

r   *■  — 

c 

r  11  — 



■z 

— 

^_    _.^ 

'/j 

f"t; 

1 

'■ 

o.t. 

•jii 

Siipliiit;" 

•-'.  1 

Vi 

-1-  11.  :i 

III.  1- 

0=".'i(, 

-i.Hr, 

—'■>.  It.T' 

—  1.0 

Wii^liili^'tnii 

••'11. 1'.» 

>> 

—  r»'.  ys 

i:i. -;t 

*» 

-1.  1 

+'.'.  T) 

-{■0.0 

'■i\ 

('m|M' 

'.•:.:i'.' 

:i 

+  ii!;f.' 

111  1.(1.'. 

li 

—  {.r* 

— n. .« 

--I.2 

.j.» 

^Vil^ulMl^ll'u  II 

III.  ."ill 

o 

+  i-.'.:i:. 

.Ml.  1  111 

*> 

1.  1 

— ','.  .'> 

--2.2 

('lllll' 

IT.'.i'J 

:t 

+  ll.'.':i 

.V.l.'.'l 

ll 

—  I..-. 

-it.» 

+0.2 

\\(lsllill).'lii|| 

I-.',.'.- 

•1 

—  I'J.ii'.i 

l.-l 

*> 

1.0 

+•-'.  ■» 

+2.»i 

•j:i 

\\'illiMIII>lllWtl 

.'il.:i.-. 

•^ 

4-  1  •.'.••.'.■. 

:i.  17 

•* 

— d.  11 

•.'.  1 

-0.  11 

('(llll' 

.V.MU 

;f 

+  ll.i:i 

•  i    -.s 

fi 

—  \.'i 

—It.  II 

—0.8 

Siiiiliii(.'(i     . 

.Ml.  -J 

>i 

+  11.  (( 

i!-.'i 

— 0.  s 

•)  .J 

+0.0 

Alliriiiy 

I-,'.:.-. 

1 

—   V-i.'Xi 

1. 1.'. 

1 

-  (1.1 

+1  Ti 

+  1.4 

\V!i-liiiii;tip|i 

I','.  (i!» 

1 

•-    ll.l'K 

I.d.-. 

1 

— (1. 1 

+  1.-.' 

+  1.0 

'vM 

\\'illi;iMi>lii\\  n 

II..V. 

•J 

+   l-.M.-. 

.Mi.  Ill 

.. 

-(1.7 

—•J.  1 

— 0.  H 

<'il|M' 

:;-.  :i7 

Ti 

+   11.111 

111. -1 

li 

— d.  !l 

—It.  It 

+  1.2 

I.riilcll    . 

;!.•-".  1 

*> 

-    1.-.,  11 

■I-.  '.17 

>> 

— d.  ti 

+ii.d 

+  l.<i 

SuMliii^Tii 

:!■,'.  7 

i 

+   1(M> 

•i:!.  '.K 

I 

-0.  II 

—1. 1 

+0.  » 

\\  a.-liiii}.'lip|i 

■il.iti 

1 

—   11. -s 

■lit.  .V,' 

1 

— 0.  It 

+  ".•-' 

+1.1 

yri 

('il|lC 

H.  7;t 

:i 

+    Kl.'.t.'. 

r.>.  -li 

li 

— d.  (1 

—It.  It 

+d.4 

Siiiiriiii;o 

.^7.  !t 

1 

4-  ic.'^ 

'.1.  7s 

1 

— (1. '.' 

-1. 1 

+  1.1 

'.'(■ 

Williiiinslnwii 

:l■■'.^l 

;i 

+   II.IM 

.■.l.-J7 

li 

— d.  1 

— li.d 

+  1.0 

Lciiii'li   . 

•l.'..  II.". 

o 

—    11.  Kl 

:i(i.  0.". 

»i 

— d.  'i 

+lt.O 

-j-0.  !• 

-i: 

Ciipr 

17.  f'.l 

;! 

+    1(1.7.". 

•js.  7-J 

Ti 

0.0 

-II.  •-' 

+0.2 

Sniilia;;(i 

.^f . :, 

•» 

+   K'.d 

Id.  I'.i 

o 

0.0 

— •-'.  1 

+2.2 

Allmiiy 

•,'l.ti7 

I 

--  I'.'.r.i 

'.1.  .'.1 

I 

0.  d 

+  1.11 

+0.4 

'.V 

('ll|M' 

.">7.  Ill 

■,t 

+  hu;.-. 

7.  Is 

II 

+  O.Ii 

—It.  '■> 

—  1.7 

Alliiiiiy 

.">.■>.  IMi 

.> 

—  I-.'.  Ill 

.i:i.  If.' 

it 

+d.-J 

+■,'.-, 

+2. .-. 

\Vii~liiii(jliiii 

.'.:i.  '.H 

.1 

—  11. 11 

.|:i.  (k; 

.) 

+d.-,' 

+•,'.  11 

+  1.0 

ast 

Williiiiiisiiiwii 

.M.  •,'.-. 

ft 

-f-  ii.i;;t 

."..  Ill 

Il 

+d..^. 

—It. .'» 

—0.7 

( Jrciiiwicli 

:iH.iii 

.> 

-  11. -ji; 

•,':i.  (Ki 

»> 

+d.'l 

+'.'.;• 

—0.2 

SllMtilir^ci 

r.1.7 

1 

+  1(1.1 

■■!.  •.'(  1 

I 

+  d.V.' 

—  1.0 

+0.1 

Wil^llillHtdll 

III.  •.'■' 

1 

.-  ii.:!;t 

(1.  •,':! 

1 

+d.-i 

+  1.1 

+  1.1! 

30 

\Villiaiiistiiwn 

l.:si 

1! 

+  11.. -.:t 

111.  lid 

It 

+o.rt 

—It. .''. 

+  1.4 

Cape 

t':i.  •,'!• 

1! 

+   1(1.17 

lilt,  s'.t 

It 

4-0. 11 

—It.  1 

+0.7 

Saiitiftgi)     . 

.-.;t.  >' 

1 

+   1(1.  li 

•-'.  7li 

1 

+  0.li 

—  1.0 

-1.4 

AU'aii.v 

{•^.  ii'.» 

1 

—  I'^ll 

l.lllt 

1 

+o.ii 

+  \.-2 

+  1.7 

Washinplciii 

11. 1'.) 

«> 

-  II. 'Jl 

d.  17 

•J 

+  0.0 

+'.'.'J 

+  1.0 

:ii 

WilliillllSlOWIl 

.^is.  'j;» 

;"i 

+   ll.l'i 

Id.  (IS 

I't 

+'M 

—It.  i 

+  1.1 

I'lilkciwa 

n.'j'.i 

1! 

—   1.'..  .'id 

'J(i.  li'.l 

li 

+  1.--' 

+  1.  r, 

+  1.« 

lli'lsiiijjliir.s 

:!7.  ti.'. 

1 

—   l.^C.l 

•Jl.-Jlt 

1 

+  0.1 

+  i.ti 

+2.2 

CilJX' 

1(1.  7s 

:t 

+  1(1.  ;is 

•JI.7S 

li 

+  l.--i 

—II.  1 

+  I.H 

Liiilcii  . 

\>\K  (i7 

:i 

—  11.11 

1(1.  lid 

;i 

+  1.'-' 

+4.2 

+2.2 

Saiiliajjd 

:!(>..'. 

1 

+    10. '.i 

•1(1.  lit 

1 

+0.1 

—  1.0 

—0.2 

\Vasliiiif,'toii      . 

r.  1.  IS 

»» 

—  11,  oil 

■Hi.  1»-' 

o 

+0.  H 

+2.  2 

+  1.1 

Nov. 

1 

Williaiiistowu 

Xi. 'Jil 

ft 

+  ii.:i-,' 

■17.  1.-. 

it 

+  1.1 

—II.  4 

+  1.1> 

I'ulUiiwa     . 

'            I-.'. '.Ml 

;! 

—  i.-..;ii 

.--.s.  IS 

It 

+  1..^ 

+4.ti 

+  1.7 

('m|ic 

i        4:!.ii'j 

;i 

+  Id. ',".• 

Mi.  dl 

It 

+  i.r. 

—II.  1 

— (l.l» 

Saiiliaijo 

:t.r, 

1 

+   10. -J 

lli.tl-J 

1 

+0..-. 

+  1.0 

—0.  2 

AUiany 

•,'v!.  lid 

1 

—    11. SS 

1V!.-J,-. 

1 

+0. .', 

+  1.2 

+  l.ri 

2 

lli'lsiiij;l'or.s 

'■i'jf-i 

.> 

-  I.v,".t 

Id.s-i 

2 

+  i.'J 

+11.  1 

—l.S 

Capi' 

'u.  1(1 

11 

+    Id.  •,'(! 

7.71 

'i 

+  i.'.i 

—2.  0 

+0.8 

Sniitiiigo 

i:i.  7 

I 

+    10.  1 

•_'l.  •-'(■> 

1 

+0.(i 

—  1.0 

+0.  r. 

Wasliiiifrtmi     . 

:!i.:i(; 

o 

—  10.  s:, 

•i  1 .  ( IS 

i> 

+  i.'.i 

+2.2 

+1.1 

a 

Williainstiiwn 

11.  ii<) 

•> 

+  11.11 

11.(1(1 

>j 

+  l.it 

o_  o 

-f-o. '.> 

('a|if 

.".7.-j:i 

•J 

-j-  l(».  I'J 

"..  Ill* 

>> 

+  1.1 

—2.  0 

—2.7 

(iivcuwicli 

s.  itC, 

T 

-  in.  117 

r.(!.  •,';> 

l' 

+0.7 

+  1.4 

+  1.2 

Saiiliapro 

i>.  (t 

1 

+    10.0 

IS.  .1(1 

1 

+d.7 

—  1.(1 

—0.  r. 

\Vasliiii;;ti)ii 

'2->.  •>(•, 

1 

—  ld.7:i 

l.">.  (Mi 

1 

+0.7 

+  1.1 

+0.  Ti 

11 

Helsiiifjt'ors 

(■>.  :!•-' 

•j 

—  I4.il(i 

51.77 

0— •.'n.^ 

+  l.(i/i^ 

+H.  Orr' 

-f-o.  8 

AND    TIIK    KMIMKNTH    WlllCll    DKl'KNU    UTON    IT. 


ll» 


Tn'^itiiif?  tlit'se  t'(|iiiitioiiH  \)\  the  iiutli(Ml  of  lourtt  si|Uaref<,  wn   linvt-  fln'  rulluwiii-   iiuimal 
oqiiutiuiis; 

First  scrii's. 

:ill     '/|-    ll.r),*,-   .•li.l-:'+l8".5  =  0, 
-    ll..V/|4.14.'->.S,j|+|ll.()r'-f  1  I    .()«(>. 

SiH,'nlii|  scricH, 

308    'h+     V>.-2;ii+\:>21i:'+   »'"..'J=0, 

G.:^/j+    41.I,J^-    l!».".l-'-    1    .:i  =  0. 

122.7'/^—    l!»!l,ir.  +  71!».(l-'  — 2')  .;J  =  0. 

Third  scries. 

a.-n    ":,+      4.s,j;,+   (i7.9r'+    :t".!i  =  (), 

4.8'/,+    :i:i.(i,J:,—    12.1-'—   7   .1=0, 

(17.!>«:,-    l2.'l,V:,  +  .'';(;7.lr:'+|;i    .0  =  0. 


FiiiirtI 


I  scrii'i 


192    '/,—  2;{.s,j,+  ^■,:>^-'  +  ^[".\  =  ^), 

-  2;{.N,/,+   217,?,,-    no-'-   !t  .7  =  0, 
(J2.1'/,-    11.0,J,+  |--'7,!lr'  +  ;i8   .4  =  0. 

Filth  srrics. 
264    «,',+    23.5,5r,—   s;J.2r'  +  7/)".l=0, 
23.5«s+    45.4,Jr,+   20.4-'+    7   ..5  =  0, 

—  83.2'/s+   2(J.4,5,+:{7^s.2-'  +  ;iS  .0  =  0. 


The  scpiinito  Holution  of  oach  worios  of  oquntioiis  ^i:;ivos  tiif  folio  win;.,'  results: 


First  seriofl  -  - 

Second  series  - 
Third  series 

Fourth  aeries  - 

Fifth  series  -  - 


«,  =  — 0.167; 
«.^=— 0.020; 
</;,=  — 0.016; 
«.,  =  — 0.188; 
'/.,  =  — 0.354; 


;:(|  =  — 0.0-53; 
,i.,  =  +  0.024; 
,J:,=  +  0.210; 
,?4  =  +  0.187; 
,jj  =  +  0.119; 


-'  =  —0.077. 
-'  =  +  0.0.39. 
-'  =  —0.016. 
r'  =  — 0.0;J7. 
r'  =  — 0.1S8. 


These  are  merely  first  approximations  to  the  values  of  the  unknown  quantities.  The  rif,'- 
orous  solution  wouldVequire  us  to  take  the  last  equation  of  each  series  and  add  them  together 
to  forma  single  one,  and  then  find  the  values  of  the  eleven  unknown  quantities  from  the  eleven 
equations  to  whieh  the  fifteen  would  thus  be  reduced.  This  we  shall  do  by  sueces.sive 
approximations. 

There  is  another  consideration  which  will  modify  their  treatment.  It  will  be  remembered 
that  /9  is  simply  the  change  in  a  during  ten  days,  that  change  being  supposed  uniform.  Now, 
having  a  .series  of  values  of  a  at  intervals  of  twelve  or  fifteen  days,  we  could,  if  they  were 
strictly  comparable,  deduce  from  their  differences  the  values  of  [i.  In  lact,  oidy  the  first  two 
are  strictly  comparable,  ditferent  stars  being  used  in  each  of  the  following  series,  the  adopted 
positions  of  which  may  not  strictly  correspond  to  those  of  the  first  series.  The  probable  dil- 
ferences  between  tlie  means  of  eight  stars,  several  of  which  are  common,  is,  however,  so  »mall 
that  the  values  of /?,  deduced  by  ditferences,  can  hardly  be  appreciably  in  error  from  this  cause. 


li 


20 


INVESTIGATION    OK    TlIK    DISTANCE    OF    THE    SUN 


Tlui  coiiipiirisdii  of  tilt'  live  siicccssivo  values  of  «  give  tlio  tollowiii^  vuluos  of /9,  iilongside 
ol'  wliich  \vu  pliiee,  for  comparison,  liie  values  wliicli  liave  just  been  derived  from  the  equations. 

Viiiuc  of  i^i  from  (litrcn.'uces  ia   +0.0(1;     from  equations,  —0.05. 
,Ja  "  "         +0.0.'.;         "  "         +0.02. 


1% 


—  O.Oo; 

—  0.12; 
-0.12; 


+  0.21. 
+  0.19. 
+  0.12. 


The  contrary  progression  and  contrary  signs  of  the  two  systems  of  valiMs  are  a  little  sin- 
gular. I  can  attribute  them  only  to  accidental  errors.  From  the  two  series  are  deduced  the 
following,  as  the  most  probable  values  of,?: 

,5,  =  +  0.04, 
,-r.^  =  +  0.04, 

!h=    0.00, 

,?4=— O.ll.'i, 

,'J5=— o.o;j. 

A  second  approximation  to  the  value  of-'  gives 

r.'=  -0".05. 

Substituting  these  values  of  ,9  and  T^f  in  the  iirst  equation  of  each  series  we  have  the  fol- 
lowing values  of  a; 

// 
«i=— 0.160, 

«2=  +  U.0]l, 

«3=— 0.002, 
«4  =  — 0.219, 
«5=. -0.205. 

These  values  of  a,  and  the  above  of /3,  being  substituted  in  the  last  equation  of  each  aeries, 
these  equations  assume  the  following  form,  and  give  the  following  values  of  tlie  solar  parallax: 


Fir,st  series    - 
Secoud  series 
Third  series  - 
Fourth  scries 
Fifth  scries    - 


Tlie  nrobable  error  of  each  equation  is  about  0".  82;  the  probable  error  of  the  concluded 
v:\\vM  of  ;:'  is  approximately  equal  to  the  quotient  of  this  quantity  by  the  square  root  of  the 
coefiicient  of  -'  in  the  llmil  equation,  or  0".016;  the  probable  error  of  ;:  itself,  therefore,  is  by 
the  usual  method,  0".014.  But  this  method  presupposes  that  the  errors  of  all  the  separate 
equations  avc  entirely  independent — an  unsafe  hypothesis  until  wo  ascertain  whether  the  obser- 
vations made  at  each  Observatory  may  not  be  affected  with  errors  peculiar  to  the  observer. 
This  we  do  by  substituting  in  each  equation  of  condition  the  concluded  values  of  the  unknown 
quantities,  taking  the  algebraic  sums  of  the  residuals  of  the  equations  belonging  to  each  Obser- 
vatory, and  dividing  by  the  sura  of  the  numbers  by  which  the  errors  of  observation  have  been 


II 

// 

II 

5.33.9r'  =  —   51.5; 

-'  =  —  0.096; 

-  =  8.815. 

719.6-'  =  +   24,8; 

+  0.034; 

8.930. 

567.1-'  =  —    12.9; 

-0.023; 

8.880. 

427.9?:'  =  -   25.1; 

-0  059; 

8.847. 

378.2-'  =  -   66.0; 

=0.175; 

8.744. 

2626.7-'  =  — 130.7; 

;:'  =  -0.050; 

:r=8.855. 

V 


AND    TIIK    ELEMENTS    WHICH    DEPEND    UPON    IT. 


21 


multiplied,  which  is  tlio  Hiinie  a.s  tho  sum  of  tlic  cuofllcitMits  of  «.     Tiio  following  iin>  the  scpii- 
rate  Hums  of  residuals  and  multipliers  for  each  series  of  e(iuatioiis,  with  tho  tiual  rueau  residual  : 


Willimnstowii.        Piilkuwii,         lli'lsiiii;t"is. 


First  series  .     .     . 

+  !!.(» 

•J.-) 

—  •-'.  '.t 

2(1 

-   II.  1 

1 

Second  st>rips 

+  '■i.  ti 

2:! 

—  K  :t 

2H 

+(l.l» 

t'> 

Third  serii's  .     . 

+  •^••l 

-2'> 

—  :>.', 

1« 

+(i.:t 

1 

Eourtli  series     . 

+  -i.:, 

It) 

—  (1.5 

"'■J 

—1.:! 

4 

Fifth  series  . 

+  -'.  1 

•,»:i 

+   1.1 

(} 

—(!.>' 

.'■. 

Sum     .... 

+1  .-..•.> 

li> 

—  l(i.  1 

111 

—  I.ll 

-,':! 

\ 


Cape 
+  2..^. 

+  r,.,-, 

+  (1.4 

—  :!.4 

—  7.() 

11 

:i4 

Leiden. 

First  series   . 
Second  series     . 
Third  series  .     .      . 
Fourtli  series     . 
Fifth  series  . 

Sum     .... 

+  :?.  4     7 

—  (1. 1    2:i 

—  ().;t    14 
+  i.:i    Ki 

—  -  2.  1      7 

—  -i.  <■) 

114 

+  (i.4     ()7 

Greeuwu 

h 

— ;{.  1 

() 

+(!.(> 

-fll.  1^ 

— 1.;» 

4 

o 
•> 

—(1. 1 

:! 

Santiaf 

fO. 

2:! 
11 
11 

14 

i 
All>iiiiy. 

„ 

-11.4 

-  4.9 

-f-2.8 
+  2.1 

—  X  4 

1 

+  ^.  1     12 
4-  H.'.t      4 

-i  4.7     :j   • 
4-  2.9     ;» 
-j-  .'>.(■)     () 

-14.  H 

(is 

+2.").  2    28 

■  - 

1 

Wiishington. 

+•-»■ 

•) 

14 

— ('. 

H 

i:t 

—II 

,'» 

11 

+<» 

2 

7 

4-'' 

0 

1(> 

4-<i 

1 

59 

First  series  . 
Sceond  series 
Third  series  . 
Fourth  scries 
Fifth  series  . 

Sum     - 


Thg  probable  alf.!;ebraic  sum  of  the  residuals  on  the  hypothesis  of  no  constant  errors  pecu- 
liar to  ecch  Observatory  will  be  0".82-v/N;  N  being  the  number  of  observations,  and  the  mean 
value  will  be  0".9TVN. 

The  following:  table  exhibits  a  comparison  of  the  actual  and  probable  sums,  and  the  actual 
and  probable  mean  residuals  of  the  individual  observations  in  the  entire  number  made  at  each 
Observatory: 


Observatory. 


Willianistown 
Pulkowa  -  - 
llelsingfors  - 
Cape  -  -  - 
Leiden  -  - 
Greenwich 
Santiago  -  - 
Albany  -  - 
Washington  ■ 


Prol)able 

Actual 

Probable 

sum. 

t:uni. 

inciiit. 

" 

// 

±5.8 

4-15.2 

±0. 05 

±4.  5 

— 1().  1 

:l-.0.  (15 

±3.6 

—  0.1 

±0.  1(5 

±.5.  4 

-  2.  () 

±0.05 

±4.4 

4-  (>.  4 

±0. 07 

±:j.o 

-  3.7 

±0.  18 

±5.7 

-14.8 

±0.  08 

±4.3 

+25. 2 

±0.15 

±4.9 

+  t;.i 

±0. 08 

Actual 
mean. 


+0.  14 
—0.  17 
—0.  04 
—0.  (12 
+0.  10 
—0. 22 
—0. 22 
+0. 90 
+0. 10 


It  will  be  seen  that  the  actual  exceeds  the  probable  residual  in  seven  cases  out  of  the  nine, 
80  that  the  probability  in  favor  of  systematic  dinerences  is  very  great.  In  the  case  of  Albany 
the  evidence  in  favor  of  extraordinary  systematic  difference  is  indisputable,  the  observed  polar 
differences  being  nine-teutha  of  a  secuud  less  than  those  of  the  other  northern  Oli.sorvatorioa 


22 


INVKSTKiATION    OF     TIIK    DLSTANCK    OF    TllK    SUN 


tlirou^''li(iiit  tlif  ("iitirt"  xM-ii's.  'I"lii>-  jiicat  iliscr('|iaiic_v  >;'ivfs  rise  to  tlie  (|iierition  wlu'ther  the 
oliscrvatiiiiis  fxliiliitini;-  tlicm  nii;;ht  imt  to  In-  cdiisiiliM-ed  iis  aiViH-toil  witli  some  ahiioriiial  source 
of  error,  and  rcjei'tcil  I'lilirely;  or,  in  oIIilt  words,  \vlu'tli(!r  tliat  standard  to  wliicli  the  tlireo 
Hoiithcrn  Ohscrvatories  is  coniiiarahle,  is  more  likely  to  be  the  mean  of  all  the  northern  Obser- 
vatories, ineludiii;;  Alliany.  or  only  the  mean  of  those  five  which  ajj,-ree  widl  between  them- 
selves.     RejeetinL;-  Albany  alto^'ether,  tlu;  final  e(|nation  in  -'  would  be,  a|i|iro.\iniately, 

•io74-'  =  -f)7". 

The  resultin,!j,-  [w.-iilax  would,  tiierelore,  be  ^' .8G(J,  the  Albany  observa tioifs  entt'ring  into 
the  final  n-snlt  for  paridlax  with  a  wcij^ht  of  oidy  one-fiftieth  that  of  all  the  others.  I  think  we 
ina\  consider  them  eiilithd  to  this  weight  notwithstanding-  their  discordance,  and  shall,  there* 
fore,  considci'  tfic  jiarallax  already  deduced  the  most  probable  result  of  the  meridian  ol)servations. 
OwiiiL;-,  however  to  tlu'  evidence  of  constant  errors,  the  |)r()bable  error  of  the  result  must  be 
increased  to  0".<)"J(l,  .uiviim',  as  the  parallax  from  meridian  observations  of  Mars,  made  in  18G2, 
accordinj;'  to  Winnec!<e's  plan. 

8".855:l:()".0ri0. 

S   <!• 

Mici-iiiiidriv  Ohsi  rralldiis  (if  Mars,  18G2. — Tiieso  observations  are  discussed  by  Professor 
Ilall,  in  tjic  Introiluction  to  the  Washington  Observations  for  ISd.'},  in  a  manner  whicli,  so  far 
as  I  sec,  leaves  notliint;'  to  be  desired.      1  shall,  therefore,  accept  his  result,   wiiich  is 

8".842iO".04, 

tlie  prolialde  i-rror  beinsj.- a  rouLijh  estimate  fro\n  the  discordance  of  the  results,  and  the  probable 
systematic  errors  of  tiie  observers. 

Si>l(ir  Ptn-allti.r  from  Ohf<frv<'(l  I'ltrulhiclh:  liicqiialily  of  the  MihiH. — The  observations  of 
the  Moon,  especially  the  older  or.i's,  do  not  present  values  of  the  parallactic  inecpiality  as 
accordant  as  \\■^^  might  I'Xpeet  from  their  number.  In  his  second  memoir  on  the  corrections  of 
the  elements  of  the  .Moon's  orKit,  the  Astronomer  Royal  finds,  from  all  the  Ureenwich  meridian 
observations  of  tlu'  ]\Ioon.  from  175(1  to  ISol,  the  value  122". 79,*  while  the  .Vltazimnth  oi)ser- 
vations  alone  give  the  value  12')". ."jO.  When  the  observations  previous  to  ISll  are  rejected, 
owing  to  uncertainty  what  value  of  the  semi-diameter  should  i)e  used,  the  result  is  increased  to 
124". .'57.      Finally,  it  is  conclinled  that  the  real  value  of  the  coefHciont  cannot  be  far  from  124". 7. 

Hansen's  discussion  of  the  (Jreenwich  observations  appears,  however,  to  have  led  to  a 
..laicriallv  ditVerent  ri'sult.  In  calculating  the  coeflicients  of  the  lunar  pert  irbations,  he  found, 
from  an  assumed  solar  parallax,  the  value  121".3GS.t  By  comparison  with  observations,  how- 
ever, it  results  that  this  value  of  the  ineiiuality  must  be  multi|ilied  by  the  factor  l.()3.)73,  in 
order  to  satisfy  the  oi)scrvations:[:       This  gives  for  the  true  value  of  the  coe.Hcient.   12")". 70. 

The  comparison  of  these  publicatiiuis  of  Professor  Hansen  shows  that  tlieso  coeflicients  are 
those  of  the  development  of  A/*'  disliirlicd  incnn  (tniiiunh/,  while  the  usual  development  is  that  of 
the  true  Umijitnih.  They  cannot  be  coinpareil  with  other  values  until  they  are  reduced  to  the 
latter  development.  If  we  repiesent  by  c,.  c^,  etc.,  the  coeflicients  of  sine  mean  anomaly,  sine 
2X  mean  .Tnomaiy,  etc..  in  the  development  of  the  true  anomaly,  we  find  the  following  value 
of  the  perturbation.s  ot  the  latter  from  the  formnhe  on  page  3  of  Hansen's  tables: 

(7/'=        n'5c  [  1  +   f  1  i'(i.<  A'+^c-i  cos^  '^g-\-  etc] . 
-|-(«')c)'^[    —  Jci  sin  if— Srj  sin  2g—  etc]. 


*  Momoirs  of  tlie  K  .yal  Astronoiiiiciil  Society,  vol.  xxix,  p.  1(5. 
tMoiiilily  KofuTs  K.  A.  S.,  vol.  x.\lir,  p.  'J4'-';  Tublos  do  lii  Lutic.  p.  H. 
!  Monthly  Notices,  xv,  <• ;  .\X1II.  'iM:  XXIV.  1(»;  Tables  ilc  In  Luiie,  p,  Iti 


AND    THE    ELEMENTS    WHICH    DEPEND    IH'ON    IT. 


23 


If  we  represent  by  a  sin  N  any  term  in  mh.  there  will   resnlt   in  oj\  in  virtue  of  tlie   lirsl 
term  of  tliis  equation,  the  terms 

«  sin  N  +  Ar,  s^in  (X+ir)  +  A''i  >*'"  ('S-i!]  +  r-:  i^iii  (X-|--V)+  I'tc. 

The  powers  of  «52  are  to  he  developed  in  like  manner. 

In  developing  the  square  of  mh,  1  lind  no  ffruis  which  will   sensilily  alTcct  the  parallactic 
inequality.     The  latter  will  therefore  depend  altou'etlier  in  tin;  f)llowin^'  terms  in  Hansen's  u(h: 

—  ll".692  8in  (—§•'  +  ('»  — f/)')  producin;,''  the  cncflicicut       ((".till, 

—  12l".;iG8siii  (ir— i'-'  +  f..-  — (//)  "  "  12]".;J(;s, 

—  V'.6Uii\n(2g  —  <;'+o,  —  ,„')  ()".0S!). 

The   total  value  of  the  theoretical  coellicients   is  therefore    12'2".09*^,  whicli,  heinj;   midtipliecl 


bv  l.();}57;i  gives 


126". IG 


for  the  actual  value  of  the  parallactic  inequality  dediieeil  by  Ifansen  from   the  observati  ms  of 
Greenwich  and  Dorjiat,  ami  adopted  in  his  tables. 

The  Monthly  Notices  of  the  Royal  Astrononiieal  Society  for  May,  18(!7,  contain  a  short 
abstract  of  a  paper  by  Mr.  Stone,  in  whicii  he  deduces  from  •2,07.')  Cireenwich  observations  the 

value 

I2.5".;{r). 

This  resnlt  I  shall  accept  as  the  definitive  restdt  nf  the  Circenwicli  observations. 

The  Wasliinfi'ton  observations  of  the  Moon,  troin  1H(I2  to  18(1.'),  inclusive,  an'  re;,Mdarly 
compared  with  Hansen's  tables.  I  have  discussed  those  maile  within  two  days  of  tlie  time  of 
maximum  and  minimum  parallactic  inequality,  on  the  supposition  that  thi;  ellect  of  errois  in  the 
other  inequalities  will  destroy  each  other  in  the  course  of  the  four  ye.irs.  Thus,  the  following 
corrections  to  Hansen's  parallactic  inequality  are  ol)taiiied  for  the  s(!V(;ral  years: 


18G2, 
ISGIJ, 
1SG4, 
18G.>, 


•)  ■> . 

— •■-' ) 

')  •> . 

-2.0  ; 
-2.0. 


These  results  are  still  subject  to  correction  for  adojtted  senn'-iliai.ieter  of  ^[oon.  Seven  transits 
of  both  limbs  of  the  nearly  full  Moon  were  observed  during  tin;  above  period.  The  it.ean  cor- 
rection to  Hansen's  s(?rai-diameter  was  zero.  If.  then,  we  suppose  this  same  semi-diameter 
applicable  to  the  Moon  at  her  first  and  last  (juartcrs,  the  coeflicient  of  parallactic  ine(piality 

will  be 

126".46— 2".]0=12l".;{6. 

But  the  same  semi-diameter  will  not  be  applicable,  because!  one-lialf  the  oliservations  for 
parallactic  ine(iuality  are  made  while  the  Sun  is  above  the  horizon,  and  a  considerable  fraction 
of  the  remaining  half  are  made  (hiring  twilight,  while  thos(>  on  which  the  semi-diameter  depends 
are  made  at  midnight,  when  the  brilliancy  of  the  Moon  is  such  as  to  excite  the  eye  to  a  dis- 
agreeable extent.  Prom  the  experiments  of  Dr.  Robinson,*  and  the  researches  of  Mr.  IJreen,t 
and  other  data,  it  .seems  that  the  eflect  of  this  brilliancy  is  to  in(M-ease  the  afqiarent  semi- 
diameter  of  the  Moon  by  about  2".  About  one-half  of  the  observations  being  thus  aOected^ 
the  correction  to  the  parallactic  inequality  from  this  cause  ought  to  be  about  -|-l".(). 


'  Memoirs  Royal  Astronomical  Society,  vol.  v. 


tGreeuwidi  ObHerv»tions  IVir  IstM,  Aj)poiidix. 


24  INVESTIGATION    OF    THE    DISTANCE    OF    THE    SUN 

To  obtain  an  iiidcpi'iiilt'iit  (Ictcrniiiiiitioii  of  this  (•(irr"ftioii,  1  liavo  niado  a  f:;oiieral  com- 
l)arison  of  tlio  apiiariMit  errors  ol  Hansen's  lables  in  rii^^iit  as(;(3nsion,  wlien  tiio  ol)servati()n8 
wore  tnado  durinj^  daylijilit  witli  the  eorrespondin;^  errors  when  tiioy  wero  made  at  nij^ht.  The 
selected  ni^lit  honrs  were,  on  the  averaj^e.  a  very  litth;  nearer  to  midnight  than  the  day  hours 
were  to  noon.      Th(!   results  were;  lor  tlie  apparent  errors  of  the  tables  in  right  ascension: 

.V 

Hefore  sinit«'t — O.lfj'l 

Alter  l)ri>;lit  (layliglit  in  the  evening — 0.0f)3 

iJcforc  liriglit  (layliglil  in  the  morning -f  0.091 

Alter  sunri.-<i -t-O.lo.'] 

From  this  investigation,  the  real  enlargement  would  appear  to  bo  0".92,  and  the  correction  to 
tlie  parallactic  inequidity  ()".;').  lint  this  correction  is  so  affected  by  the  correction  of  the 
(•oellicient  of  variation  that  it  cannot  be  relied  on. 

There  is  still  another  cause  of  smaller  apparent  diameter  about  srnrise  and  sunset.  At 
those  times  the  Moon's  disk  is  generally  very  sharply  delined,  while  at  midnight  there  is  gener- 
ally more  or  less  spurious  eidargement,  called  "blurring." 

Finally,  the  following  are  adopted  as  tiie  most  probable  corrections  to  the  semi-diameter 
at  midnight: 

// 
On  accou'-.i  of  irradiation — 0.9 

"  "      gijmrioufl  enlargement — 0.2 

Total -l.l 

The  effect  of  this  t'orrection  will  be  to  increase  the  parallactic  inequality  derived  from  the 
Washington  observations  to 

125".46. 

The  (lilVerent  results  will  be  combined  by  giving  this  the  weight  4,  Stone's  tlie  weight  8, 
and  Hansen's  the  weight  1  ;  the  latter  being  derived  from  tlie  Dorpat  as  well  as  the  Greenwich 
observations.      This  gives 

125".49 

as  the  most  probable  value  of  the  parallactic  inequality  derived  from  observations. 

Owing  to  the  uncertainty  respecting  the  proper  semi-diameter  of  the  Moon  to  be  adopted, 
and  to  the  fact  that  owing  to  the  libration  of  the  Moon's  disk  the  points  of  the  Moon's  surface 
observed  at  quadratures  may  be  systematically  dilferent  from  those  observed  at  full  Moon,  I 
estimate  the  probable  error  of  the  above  result  at 

0".3.'5. 

To  deduce  the  solar  parallax  from  this  value  of  the  parallactic  inequality,  the  formulas  of 
Delaunay  and  J^lana  will  be  ado()ted.*  They  give,  for  the  parallactic  inequality  in  terms  of 
the  solar  parallax, 

^'•r+^sinr(i-0 

*  Thcorie  ilii  mouvoro»>i>t  >Ie  la  Lii'ie,  tome  II,  p.  847.     Mr.  Delaunay  was  good  enough  to  communicate  the  formulsR 
lor  F  ill  aJvuncf  of  tho  volume. 


i 


AND    I'HK    KLKMKNTS    WHICH    DEPKNU    ll'ON    IT.  25 

WImt. 

,T;=:  ciiiislaiit  ot    -iA..v  piirail.ix. 

//—^iiiiiss  III'  llif  .Mimii.      Adiiptcil  \iiliir,    ^^'  .. 

/'::;=  fuiistant  nl'   liiliiii-  |iaialla\.  =  .'!  I 'J'J".  i. 

//'=:  ratio  III    iin'aii  iiMlinii~  nl    Sim  ami  Mimii. 

/''.  a  lat'tiir  wlmsr  vahu  ,  a  rn  nil  in;;-  In  i>i'lailiia\ '  ^  tlicnrv.   is  rii|-iiii''l  as  Inllnws: 

'I'crins  iiiililililird  1)V  />/ O.l.SMJ.i 

in'  ■     - .()(;")(){> 

"  m' A):i2t\:^ 

///'--- .OOSS") 

m'' .(i(i;;^-j 

in"   -      - .0(11. !(; 

///■ .(KKKil 

IligliiT  trniis,  ;  iiy  iiidiu'tiini  1 .()()0:J!t 

'I'otal  valiif  iif  F .-ill-.':; 

VVliciico,  snlar  parallax  I'mm  paiallactic  iiiri|iiality  of  tlic  .Mnnn  =. 

S".S38  L  0",()rj.>. 

As  a  test  of  tlio  tlieory,  this  nvsull,  may  liu  rnmparcil  with  that  of  Hansen,  in  tlie  Monthly 
Notices,  vol.  24.  From  a  value  of  the  Moon's  mass  -J~,  and  the  parallaetie  ineipiality  of  his 
tables,  (12«".4G,)  ho  finds  for  the  solar  8".'J16.  Alterintr  the  result  to  corres|)ond  to  the  data  of 
the  prcsont  paper,  it  will  be 

S".Si4. 

agreeing"  satisfactorily  with  the  theory  of  Delannay. 

S  8. 

Solar  Poralldx  from  t/ic  Ohstrvcd  Linuir  lujnoflon  nf  lltr  A'arf/i  coinhincil  with  the  Mdsft 
of  thr  Moon. — In  constructinp;  his  tables  of  the  Sim,  L''  Verrier  inv(;stigated  the  lunar  inequality 
of  the  earth  from  35  years  of  Greenwich,  42  of  P'  ,  i.s,  and  17  of  Konigsbery  observations,  with 
the  result* 

G''.50, 
and  a  probable  error  of  aboiit  0".03. 

To  complete  tlie  investigation,  1  have  added  the  results  of  14  years  of  Greenwich  and  T) 
years  of  Washington  observations.     The  results  for  the  separate  years  are  as  follows; 

GrcenivU'h  OhsirrnlionN. 

n  II  ti  II 

iMol.  (Jiir.  =  +  0.;J.'{;      iiii'(|,  =(i.87.       IS.JS.  Cur.  =  +  0.01  ;      iiicip  =(;.l-"i. 

\H[)2.  — o.i;_j;  G.ii.     isr.n.  +0.21 ;  g.().'). 

is/;;!.  4-0 -^.'i;  0.79.       lS(iO,  +0.1(i;  (J.(JO. 

l^io4.  —0.11;  (i.:r,i.     isiij.  -o.:jo;  <;.io. 

is.jo.  +0.0;{;  G.47.      JSO-;;.  +0.i!2;  6.70. 

18,5(i.  -|-0.;J!>;  G.8:j.  j    ISG-i.  +'».ll;  G.tio. 

1857.  -O.IO:  <;.;J1.       1S61.  -0.0:>;  (i.lH. 

Resulting  value  of  the  lunar  inecpudity, 

6".56±0".04. 

'  Animli's  cl<>  rOliscrviitiiin'  Iiii|iiiiiil  ili-  I'liris,  Miiiiijiri-s,  tome  i\,  p.  Kill. 
4 


■_*()  IMVKSIKJAI  lO\    OF    TlIK    1  US  lANCK    OK    Till;    Sl'N 

//  iislii mititit  Oliy(  vrnfiiiHS, 

//  It  n  It 

JsCI-'-j.  (',,!■. ——(1.0  I  ;    iu,'(|.  =:(i.:!7.      |S(il.  ("i.r  =— 0.01  ;     ini'i|.  =f).10. 
ISC,;;.  4-0..'",:  (i.(;s.     isi;,-,.  +n.lS;  g..')0. 

Ki'i-nltiuu'  viiliic  nl'  ihc  lMii;ir  iinMiualit}", 

iV'.ra  I  o".o;. 

Il  w  ill  lir  seen  \\\,\[  till'  I'dlldU  iiin'  Viiliics  <)l'  tlic  taln.Lr  cocllicicnt  have  Ix'cii  used  in  ulitain- 

iiiii'  llic  in('i|iialily  fniiii  ihr  (•(iircctidii  given  liy  tin'  (iliscrvations; 

// 
(  Jim  (iiwifli,  I  *>.)l-lsr):)  -  (5  ;j  I 

|s,vl-lS(;o (i.ll 

iMil-lfSO:! (J..')  I 

isoi (;..')0 

AVa.^iliiii;.'!!!!! (i..)! 

Il   i-  ncci'.-'^ary  fo  explain  Imw  tlu'.-<i!  values  have  liecii  nlitaioed. 

Tlu'  aliove  euirections.  in  the  ease  of  (rreenwieh,  were  dedueeil  IVoni  tin'  "Apparent  Krntr 
nl'the  Tables  in  K.  A.."  given  each  year  in  tho  (ili'eenwieh  ()lis(.'i'vations  in  eiinoectiini  with  the 
(tl>.-irveil  positions  1)1'  the  Snn,  l>y  a  e()ni])aris()n  nl'  the  "Apfiai-enf  Erroi's  "  within  three  days 
of  tin'  nia.xinia  and  niiniinti  values  ol'  lunar  ineipiality.  The  next  sto|)  is  to  find  the  valiu?  of 
the  ineipiality  actually  contained  in  tlie  eplienieris.  The  latter  is,  until  lS(j.'>,  that  dedu(;ed 
tVniii  Carlini's  Tallies  and  pnldished  each  year  in  the  IJritish  Xaiitical  Almanac.  Hv  induction 
from  Cai'lini's  Talde  V,  it  appeared  that  his  value  ol'  tlu'  ineipiality  was  O"..")!.  Afterward,  1 
ioiind  that  in  a  |ireceiling  vohune  of  the  "  KiVemerides "'  lie  had  deduced  the  value  ()".').'{7 
Irom  theory,  and  probaldv  the  table  was  constructed  from  this  value.  If,  ttii'ii,  the  ephomeris 
('orres|u)nded  exactly  with  the  tables,  this  would  be  the  value  to  which  the  corrections  correspond. 

l>iit  on  jingc  V  of  oa(di  voluini^  of  tlio  Nautical  Almanac  from  1854  fo  ISOO.  inclusive,  it  is 
slated  that  "The  Longiliide  and  Radius-Vector  have  been  computed  accurately  from  the  Tables 
lor  the  .Moan  Noon  ol  e\ery  (Jth  day  of  the  year,  and  iiitiM'polated  with  'oiii-lh  dill'erences  for 
each  day."  Now,  since  the  lunar  inequality  goes  through  its  period  in  a  month,  its  successivo 
orders  of  dill'erences  for  eat'li  sixth  day  will  bo  divergent,  and  interpolation  with  fourth  dilTer- 
eiiccs  will  result  in  the  interpolated  iiie(iuidity  lieing  generally  too  small  numerically.  To  find 
how  much  too  small.  a<'tual  trial  was  resorted  to.  A  number  of  six-day  series  of  values  of  tiio 
ine(|uality  was  taken  from  Carlini's  'I'able  V,  interpolated  to  days  near  the  maxima  and  minima, 
and  compared  with  the  corresponding  tabulai'  values.  Th(>  result  showed  that  the  interpolated 
values  were,  on  the  average,  numerically  too  siuall  by  0".  10.").  .^iiico  one-sixth  of  tho  values 
would  be  accurate,  the  actual  tliminutioii  of  Carlini's  iiiei|Uality  would  be  (>".6n7,  reducing 
it  to  O".!'). 

From  1S5S  forward,  the  Sun's  positions  given  in  the  American  K|)h(>meris  art;  deduced  from 
Hansen's  'I'ables,  in  which  the  value  of  the  lunar  inequality  is  S  ".  1 1 .  Comparing  thes(!  positions 
with  the  corresponding  ones  of  the  N:ioti<cl  Almanac,  the  following  din'ereiicc.s  were  found: 

// 
^>'.  -ftLOn^: 

;    •>■■'  +(1.(1.1: 

-f  0.01  : 

Mean,    -f  0.02  : 
giving,  for  the  v.due  of  the   inequality  actually  cnntained  in  the  N.iutical   .Almanac   Eplietneris. 
(•".4.'{.      The  mean  of  this  and  tiie  former  result  is  6". 44,  which  was  considered  the  must  prob- 
able value  of  the  quantity  in  question. 


AND    TIIK    Kl.KMKMS    WHICH    Dl'.l'I'.Nlt    ri'ON    11'. 


27 


Witlinut  the  limits  ol'  tlic  scwcii  yciirs,  18r)4-'GO,  tlic  (•'iiiipiihitions  i\\'  tlu^  N'aiilic;il  AIiiciiiik; 
iiro  prohiiltly  ut  sulllcicntly  short  iiit(>rs-;ils  fo  avulil  |iic  n-nir  of  intcf|)  'lilion. 

For  ISIM,  licVorritM-'s  Sohir  TaliK's  wrrc  ailoptiMl,  (li(>  value  of  i  he  lunar  t'i|iiatioii  in  wliifli 
is  ()".;")().  We  liavo,  tluMi,  tlio  foljowin;:  tlirco  valiuvs  of  tlic  (|iiiutity  soii^li'  for,  (IciIiu'imI  from 
obsi'rviitions: 


Knim  (in'finvicli,  I'iiris.aiid  lvc>iiii;^lii'r<j;  nlp-icrvatioii:*,  ()..')0     )().().; :   \vt.— II. 
(ircciuvicii,  18;')!  to  ISdl f...',i;     |  0  0 1  ;  C. 


War^liiiif^toii,  I8<")1  to  l^O;') 
lIi.'fMi,  l)y  wci;;!itt<  -     -     -     - 


-  (■>..'»  I     I  (\M', 


{\.'>2l)  \  ovs.;. 


Altli(Mi;j,li  flie  aocidiJiitiil  errors  of  tin;  oliservutioiis  on  wliicli  \\\'\<  rcsnlt  ilt'iicnds  arc  (piito 
liif^o,  the  observations  have  this  invaluable  (^liararteristie,  that  tlh-y  secin  to  b  ;  |)erfi'ctlv  i'ree 
from  any  eiiiise  of  systematic  eri'or.  Amoni;'  all  the  <'onstant  sources  of  (>rror  to  which  ob- 
Kcrviitioiis  of  the  Sun  ;irc  liable,  I  can  think  of  noni!  whicii  can  systematically  chanats  with 
the  first  and  hist  (juarters  of  the  Moon.  If  there  are  none,  the  precision  of  the  determination 
of  the  lunar  equation  will  go  on  increasing  indelinitely  with  the  number  of  observations. 

The  next  stt'p  is  to  determine  the  mass  of  tiio  Moon.  The  most  precise  determination  is 
obtained  by  a  comparison  of  the  const, mts  of  precession  and  nutation,  which  i;-ives  the  ratio  of 
"*  the  disturbiiif^  forces  of  the  Sun  and  Moon  in  chan<;iiig  tin;  dirct'tion  of  the  earth's  axis  of 
rotation.  The  value  of  this  ratio  will  Ite  (le(luced  fn/ui  tl\e  t'xhaustivc  memoir  of  Serret*,  afttu- 
reconstructing  his  expression  for  SJ  so  as  to  include  tin;  terms  of  tin;  tiiird  order  with  respect 
to  the  inclination  and  eccentricity  of  the  Moon's  orliit,  which  he  has  neglected.  This  is  etfected 
by  substituting  the  (Expression 

I  1  +  i!'-"^  I  sill  f  cos  )■ 

for  c  in  his  value  of  .V. 

Let  ns  i)ut 

//zrmass  of  the  Moon,  that  of  the  Earth  being  unity. 
^)=sine  of  its  parallax,  in  seconds. 
M  =  inass  of  the  Siui. 

e  =  ratio  of  disturbing  forces  of  Sun  and  .\b)on. 

/  =  disturbing  force  of  the  Sun. 
f<  =  luni-solar  [)r<!Cession  for  18")l). 
N  =  constant  of  nutation. 
Pr__  coefficient  of  lunar  equation  of  Earth. 
Then  the  oliserved  length  of  tlie  seconds  pendulum  compared  with  tiie  siderial  year  gives 

log  M7:^=:S.:Jo488. 
Whence 

Tiie  forniulie  of  precession  and  nutation  give 

rt  =  [9.96272|x  +  [0.9592a|>!£. 
Peters' a  concluded  value  of  the  constant  of  nutation  is 

N=9".223. 


'Animlt's  lit'  roh.sciviitoire  Impcriul  ili'  I'.'iris,  vol.  \,  |).  :!'.i;i 


2H 


INVKSl'ICATION    OK     PUK    niSIANTK    (»l"     IIIK    SI'N 


TIk!  Viilun  nf  llir  liiiii ■>' ill r  nirf('--i(p|i  ilrrivcil  IV.iiii  Sinnc's  -(Mh-imI  |)ri"'rssii)ii,   uilli  tlir  iiiii>-i 
III'  VuiiiiM  coiK-liKlcd  liy  lii'N'cnicr,  IVniii  his  iiivr-i  i-atiiHis  cil'  llio  molinii  of  thai  phiiiut,   is 

(I  =  :,!)". -.i'lS. 

Snlistiliitiiij;'  these  vahies  dI'  ii  ami  N  in  tho  alinve  ei|iiatii>iis.  \vu  liml 

Id;,'  >r;=l..r(Nl.S, 
In;;  /    =l.-j:{SOS. 

1.1^'  ;  =:n.:);!'.i-i(i. 
I 


N|.()f> 


DeveliipiiiL:'  the  hui^'itiide  and  paralhix  of  tlir    .Mumi  sd  as  lo  inehide  ihe  varial  ion,  and  (lie 
e()iTes|Miiidint:'  term  in  the   parallax,    we  lind 


l'=l.()(IN() 


1+/'/' 


.;.;i.i|.,-_. 


t»r. 


T=  .oKiKH  r 


(-')■ 


SiiusI  ilnlini;'  the  \-aliie  nl    !',  already  I'.amd  iroin  nliservatmn,  we  have 

rr  =  S".S()9. 

Till!  must  uiirertaiii  data  whieli  enter  intn  this  re-:ult  are  the  ennstaiit  of  nutation,  with  the 
I'e.-ultin^"  mass  nt'  ihd  Moon,  and  the  lunar  eipiation  nT  i!io  earth.  'I'he.  [)rol)al)le  error  of  tlie 
nutation  eiiiislant  is  perhaps  -v',-  of  its  whole  ainniint,  which  would  involve  an  error  of  --';--  in 
tho  resultiuL;'  mass  of  the  Moon  a?id  solar  parallax,  or.  of  U".OH:  in  the  latter.  The  unc(;rtaiiit y 
of  the  other  faetor  involves  a  prohalde  error  of  0".0,!1,  so  that  the  total  jiroliahh'  error  of  tho 
result  is  ((".OiU. 

TraiisU  of  Whuh  In  17(!!t. — The  results  of  Powalky's  discussion*  will  be  accepted.  He 
linds  -=  8". S32±0".0'2!.  l>ut  eonsidorin^-  that  the  longitude  of  the  ohsorvinj;-  station  at  San 
Jose  is  uncertain,  he  arbitrarily  chanji-es  it  by  lOv..  which  increases  the  [larallax  to  8".S(i,  which 
he  considers  the  most  probidile  value. 

That  so  >mall  a  change  in  the  longitude  of  a  single  station  should  change  the  parallax  so 
largely,  shows  that  the  piobable  error  0".021  iiiust  be  illusory.  I  think  0".()-l  a  more  likely 
value  of  this  element. 

i^   10. 

C<>i)cbi<h'(f  Parallax  and  Di-^laua' q/'  the  Sim. — The  separate  results  for  the  solar  parallax 
with  their  jirobable  errors,  and  their  conseijuent  weiglits,  are  as  follows: 


Friini  mtriilian  ohscrralidits  of  Mars,  ]>^\\:i    -      -   8.N,0r)rl:  .020;      \vf.  =:2,5. 

FroDi  miinwiifric  ofisrrraf ions  of  Mar.i,  18(j2     -   8.812:h  .040;  G 

Fro)n  jiiirdlUiiiic  invqindili/  <tf  till'  Moon  -     -      -   S.S38  I  .028;  Ui  . 

From  tl<tl  It  liar  equation  of  the  Earth  -     -     -     -    8.S09±  .054;  3. 

From  thr  transit  of  Viniri  in  MQS) 8.8(i0  I  .040  ;  6. 

From  Fowaft\s  r.rperimcnts  on  light     -     .     -     .  8.860  ?  ] 

■  Adililioii^  :\  III  Coiiimissillicr  des  TtMii))s.   I"'!'!?,  p.  •,'•,'. 


ANO    TIIK    KI-KMKNIS    WHICH    DKPKNH    ITI'ON    IT 


V 

V 


'I'lic  hisl  iii:iy  lint  In iisic|i'iT(|  ii  stiiflly  ii-l iMiiniiiiiMl  result,  an. I  it  i^  ilillicull  In  assiLiii  ils 

[irolialih'  t'lrcr.  'I'lic  lucan  hy  weights  ol'llic  ntln'i-  ii'-iilts  is  S".Sl7.  Fn>iii  a  cniisidriai  imi  <>{' 
all  tho  results,  it  is  (•(HicIikKmI  tliat  in  tin'  prcsi'iit  >lali'  ol  astroiiomiiMJ  sciiMioi'  tln'  niosi  priiliabji- 
Viilu(5  of  till)  menu  t;(|iiatiirial  hori/.oiil.it  paralliix  ol'  tlio   Sun  is 

W'.HIW, 
witii  a  prohalilu  error  of 

|-()"(il;i, 
forrospoiuliiin'  to  a  mdaii  (listaii(M>  oi' 

'.)<J,n80,000  .-latiiti-  iiiilr.-<. 
For  astvoiioiuical  iiurfMiscs  tlio  value  ol'  -, 

may  lie  talceii  as  a  iduikI  inimhiM-  of  Imiiilreilt  li>  hiLvinj;  e(pi;il  \vei--|it  with  tlii>  aliove  imiicIiiiIimI 
value. 

§  11. 

Conclusions  irspicHiu/  the  (Ulfcniil  Kl<ni"nls  irli'fh  ih innd  on  lln-  jiirnlhiroj'  t/ir  Smi. — From 
the  equation  of  ^1,  which  i;'ives  the  mass  of  the  Sim  in  terms  of  its  parallax,  we  liml  i'or  the 
value  of  that  mass 

.•viGsoo  I  i;;oo, 

talcing  the  mass  of   the  Earth  as  unity. 

The  v.alue  of  the  lunar  ei|Uation  of  the  Fartli  derived  in  the;  same  section  li'ives  for  the 
muss  of  the  ^^oon 

I 

81.44  i().;j;j' 
Taking  tho  mass  of  the  Sun  as  unity,  the  coiuhined   masses  of  the   Hiitli   and   Moon  will 
therefore  be 

^l 

With  the  above  value  of  the  mass  of  the  Moon  we  liml    from  the  e(|UatioiH  of  >;  7. 

j=a.i74. 

N=<)".:.MO  I  0"011, 

a  value  of  the  constant  of  nutation  rather  more  probable,  and  more  easily  obtained  than  any 
derived  from  direct  observation.  The  advanta^•e  of  the  theoretical  mode  of  deriviiiL;  this  con- 
stant arises  from  the  fact  that  an  error  in  the  adopted  mass  of  the  Moon  produces  an  error  of 
less  than  one-third  its  proportignate  amount  in  the  resulting  constant  of  nutation. 

The  theory  does  not  apj)ear  to  be  subject  to  any  objection  arising  from  our  ignorance  of 
the  physical  constitution  of  the  iuterit)r  of  the  Marth. 

From   the  data  of  §G,  Delaunay's   thecu-y  gives  i'or  the   parallactic   ineijuality  of  the  Moon 

12r>".(j;{4:0".19. 

Taking  the  constant  of  aberration  as  20". 445 1,  we  have  for  the  velocity  of  light 

18.5,600  mile.'*  per  Hecoiul. 

This  is  slightly  greater  than  the  result  of  Foucault's  experiments  with  the  revolving 
mirror.  Adopting  that  determination,  the  constant  of  aberration  would  ite  increased  about 
0".03.  But  tho  distance  of  tho  Sun  and  the  terrestrial  determination  of  the  velocity  of  light 
are  both  uncertain  to  an  amount  greater  than  this  increase,  which  is  therefore  altogether  unre- 
liable.     The  constant  of  aberration  must  be  found  by  direct  observation. 

0 


lA 


y? 


■J*-      ^v- 


—  •-iviiiTj^-..  ^  ^ 


s 


